Stars such as New Zealand's Martin Guptill and Brendon McCullum, South Africa fast bowler Dale Steyn, England's World Cup-winning skipper Eoin Morgan, Pakistan's Shahid Afridi, Australia's Shane Watson and Afghanistan leg-spinner Rashid Khan had all been lined-up to play.
However, organisers say that the 2019 event has "reluctantly" been postponed.
"The Board of the Euro T20 Slam, funding partners and franchise owners of this exciting new T20 tournament have reluctantly come to the decision that staging of the event will not be possible in 2019," said a tournament spokesman.
"We want to ensure that the inaugural staging of the Euro T20 Slam provides the best springboard to making this a truly flagship event on the global cricket calendar.
"As such, we believe the right course of action is to postpone the Slam to a further date. This will give us the necessary breathing space to ensure we are ready to go."
The Euro T20 Slam teams were due to play each other in a series of 33 matches from August 30 to September 22, with fixtures taking place in Dublin, Edinburgh and Amsterdam.