Tharoor, the country's junior foreign minister alleged that Modi had made attempts to pressurise the owners of the Kochi city IPL team to abandon their bid for another city.
Modi, on the other hand, revealed the names of shareholders of the Kochi consortium that brought the team for $333m.
Kochi was sold to Rendezvous Sports World (RSW) last month and along with the Pune team will join the IPL from 2011 raising the total number of teams in the tournament to 10.
Modi in a series of Twitter messages on the weekend said he was asked by Tharoor not to check the background of the controversial buyers, the Indian Express newspaper reported.
The startling claim assumed significance since one of the shareholders of RSW, Dubai-based businesswoman, Sunanda Pushkar, is known to be a close friend of Tharoor.
"I was told by him not to get into who owns Rendezvous, especially Sunanda. Why?" Modi asked.
The team is based in Tharoor's state of Kerala in southern India.
Indian newspaper reports say Tharoor is planning to marry Sunanda after separating from his second wife. Even as the chairperson of the ruling United Progressive Alliance Sonia Gandhi convened meeting on the matter, the issue snowballed into a political issue.
The main opposition Bharatiya Janata Party questioned why Sunanda who had no link with either cricket or Kerala was given a stake in the RSW. Alleging "misuse" of authority by Tharoor to "secure" investment by Pushkar and the party, Modi demanded that the minister be sacked.
In a statement issued earlier on Tuesday, Tharoor accused Modi of trying to thwart the Kochi franchise which was conducted in an "open and transparent manner".
He said he had "neither invested or received a rupee" as a mentor of the Kochi team.
"His (Modi's) extraordinary breach of all propriety in publicly raising issues relating to the composition of the consortium and myself personally is clearly an attempt to discredit the team and create reasons to disqualify it so that the franchise can be awarded elsewhere," said Tharoor.
"Contemptible efforts have been made to drag in matters of my personal life which I do not intend to dignify by commenting on them."
The IPL, currently in the middle of its third season, has become a multi-billion dollar industry, with teams drawing players from India and abroad.
The total brand value of the IPL stood at $4.13bn in 2010, according to a recent evaluation by the London-based Brand Finance Plc commissioned by India's Economic Times newspaper.
IPL team controversy
Mumbai - Indian minister Shashi Tharoor and Indian Premier League chief Lalit Modi were at the centre of a row surrounding the ownership of a new team in the popular cricket tournament, news reports and officials said on Tuesday.