The pair carded five-under-par 60s to sit one shot ahead of Lindani Ndwandwe and Chris Lloyd, who both fired rounds of 61, in the co-sanctioned European and Sunshine Tour event at Royal Durban Golf Club.
Another South African, Colin Nel, was among a group of 10 players a further stroke back on three under par.
The 1 million euro (R11.2 million) event, the first of the 2013 European Tour season, is now effectively a two-round competition that will constitute just 36 holes after days one and two were both abandoned.
Rain in the build-up and an unusual thunderstorm on Thursday left parts of the course unplayable, with four holes shortened to change the initial par-70 course to a par 65.
Clark, only just finding his game again after close to a year out with an elbow injury, was pleased with the way he set the early pace after a round that included six birdies and a bogey. He pointed to his putting as the key to his performance.
“It wasn’t that easy out there, but I was amazed at how good the greens were with all the rain they had. The greens were pretty firm and obviously great to putt," he said.
“I made some good putts and that’s really what gives me this score.
"Obviously I gave myself a lot of chances and I made some good twos on some of those par threes.”
The 36-year-old, who won the 2010 Players Championship, was happy to be in pole position and felt there was only one way to play Sunday's final round.
“Obviously we just don’t know what’s going to happen, if we’re going to play again or what, but right now you’ve got to go as low as you can and be aggressive.”
Madsen, 24, was making his European Tour debut and enjoyed what he described as a “fun” experience, saying it was “nice to finally get out and hit some shots”.
Ndwandwe, a relatively unknown South African, mixed one eagle with six birdies, one bogey and a double bogey.
Twice a winner on the Sunshine Tour, in 2001 and 2009, Ndwandwe was delighted to be in contention.
“In every tournament if you give yourself a good start you always have a chance," he said.
“Getting a good start with the big okes out there is always a boost to your confidence.”
Weather permitting, the final round was set to take place on Sunday, although play on Monday was also a possibility if most of the 156-man field could get through their second 18 holes.
Scores after the delayed first round of the co-sanctioned Nelson Mandela Championship at Royal Durban Golf Club on Saturday (Par 65, RSA unless specified).
60 - Tim Clark, Morten Orum Madsen (DEN)
61 - Lindani Ndwandwe, Chris Lloyd (ENG)
62 - Colin Nel, Matthew Southgate (ENG), Christiaan Basson, Maximilian Kieffer (GER), David Horsey (ENG), Shaun Norris, Julien Quesne (FRA), Desvonde Botes, Sam Little (ENG), Eduardo de la Riva (ESP)
63 - Richard Bland (ENG), Carlos Del Moral (ESP), Allan Versfeld, Mikael Lundberg(SWE), Bjorn Akesson (SWE), James Kingston, Pablo Larrazabal (ESP), Jaco Ahlers, Steve Webster (ENG), Matthew Nixon (ENG), Robert Coles (ENG), Marc Warren (SCO), Bradford Vaughan, Oscar Floren (SWE), Alessandro Tadini (ITA), Andrew Marshall (ENG)
64 - Espen Kofstad (NOR), Emiliano Grillo (ARG), Dominic Foos (GER) (AMA), Mark Williams, Seve Benson (ENG), John Parry (ENG), Soren Kjeldsen (DEN), Tyrone van Aswegen, David Hewan, Michael Jonzon (SWE), Rhys Davies (WAL), Richard Finch (ENG), Doug McGuigan, Estanislao Goya (ARG), Adilson Da Silva (BRA), Michiel Bothma
65 - Moritz Lampert (GER), Andrew Curlewis, Warren Abery, Jake Roos, Fabrizio Zanotti (PAR), Trevor Fisher Jnr, Theunis Spangenberg, Bryce Easton, Hennie Otto, Lorenzo Gagli (ITA), Garth Mulroy, Ignacio Garrido (ESP), Jacques Blaauw, Justin Walters, Teboho Sefatsa, Alex Haindl, James Morrison (ENG), Tyrone Mordt, Richard McEvoy (ENG), Darren Fichardt, Magnus A Carlsson (SWE)
66 - Peter Whiteford (SCO), Matteo Delpodio (ITA), Mark Tullo (CHI), Alejandro Canizares (ESP), David Howell (ENG), Branden Grace, George Coetzee, Dean Burmester, James Busby (ENG), Damien McGrane (IRL), Albert Pistorius, Andrew Georgiou, Eddie Pepperell (ENG), Peter Hedblom (SWE), Gregory Bourdy (FRA), Scott Jamieson (SCO), Oliver Bekker, Peter Lawrie (IRL), Martin Wiegele (AUT), Chris Paisley (ENG), Neil Schietekat, Ruan de Smidt, Stefan Engell Andersen (KEN), Andy Sullivan (ENG), Steve Surry (ENG), Matthew Baldwin (ENG)
67 - Jose Manuel Lara (ESP), Justin Harding, Jean Hugo, Daniel Brooks (ENG), Lyle Rowe, James Kamte, David Drysdale (SCO), Vaughn Groenewald, Simon Wakefield (ENG), Brandon Pieters, Andreas Harto (DEN), Chris Swanepoel, Thomas Aiken, Martin Maritz, Kevin Stone, Kristoffer Broberg (SWE), Neil Cheetham (ENG)
68 - Joakim Lagergren (SWE), Tjaart van der Walt, JB Hansen (DEN), Merrick Bremner, Ben Mannix (ENG), Ulrich van den Berg, Divan van den Heever, Gregory Havret (FRA), Matthew Carvell, Louis de Jager, Jaco Van Zyl, Peter Uihlein (USA), Alpheus Kelapile, Richard Sterne, Haydn Porteous (AMA), Keenan Davidse, Attie Schwartzel
69 - Thabo Maseko, Charl Coetzee, Jean-Baptiste Gonnet (FRA), Grant Muller, Scott Arnold (AUS), Riekus Nortje, Oliver Wilson (ENG), Titch Moore, Anthony Snobeck (FRA), Joshua Cunliffe, Alexandre Kaleka (FRA), Gary Stal (FRA), Keith Horne, Ockie Strydom, Graeme Storm (ENG), Christian Cevaer (FRA)
70 - Ryan Cairns (ZIM), Jorge Campillo (ESP), Jacques van Tonder, Scott Henry (SCO), Gary Lockerbie (ENG), Callum Macaulay (SCO)
71 - Ryan Tipping, Irvin Mazibuko, Alan Michell, JG Claassen, Alexander Levy (FRA)
72 - Reggie Adams, Jack Kutumane