In a statement, the artificial intelligence company said it respected Summers' decision to resign.
"We appreciate his many contributions and the perspective he brought to the Board," OpenAI said.
The news comes after both chambers of Congress agreed on Tuesday to pass a measure to require the US justice department to release its files on Epstein.
The measure will then head to the desk of US President Donald Trump for approval. He has said he plans to sign the bill, after reversing his position on the issue following pushback from his supporters.
A batch of Epstein-related emails released by the House Oversight Committee last week mentioned a number of high-profile figures in the financier's former circle, without indicating any legal wrongdoing by those figures.
The emails indicated that Summers and Epstein dined together frequently, with Epstein often trying to connect Summers to prominent global figures.
After the emails were shared with the public, Summers said he took "full responsibility for my misguided decision to continue communicating with Mr Epstein".
He added that he wanted "to rebuild trust and repair relationships with the people closest to me".
Summers held senior posts under two Democratic presidents; serving as treasury secretary under Bill Clinton, and as director of the National Economic Council under Barack Obama.
He led Harvard from 2001 to 2006 and remains a professor there. When announcing his step-down from public commitments earlier on Monday, he said he would continue his teaching commitments.
Following Summers' announcement on Monday, the Center for American Progress, a liberal think tank in Washington where Summers was a senior fellow, confirmed that Summers was no longer affiliated with the organisation.
Summers joined the board of OpenAI, which makes ChatGPT, in 2023 - following a failed attempt to oust its chief executive Sam Altman.