Distancing the party from the comments made by its leaders Pragya Thakur, Ananth Hegde and Naveen Kateel in support of Godse, Shah said the party's disciplinary committee would inquire into the matter.
"The statements made by Pragya Thakur, Ananth Hegde and Naveen Kateel in the last two days are their own statements. The BJP has no relation with their statements," Shah tweeted.
"However, they have retracted their statements and also apologized. The BJP has taken a decision to send their statements to the disciplinary committee of the party. The committee will submit a report within 10 days to the BJP after receiving the replies of the three leaders over their statements that are against the ideology of the party," he said.
The Bharatiya Janata Party (BJP) President's announcement came as the party faced criticism over the remarks ahead of the final phase of the Lok Sabha elections.
Pragya Thakur was the first among the three party leaders to call Godse a "patriot", leading the Election Commission to seek a report from the Madhya Pradesh Chief Electoral Officer.
As her statement went viral, two BJP MPs Union Minister Anant Kumar Hegde and Nalin Kumar Kateel also came out in her support.
Godse shot dead Mahatma Gandhi at a prayer meeting in New Delhi on January 30, 1948. He was hanged after a trial.