Several other U.S. Internet companies may also have been contacted as part of the investigation.
Assange blasted the moves, saying they amounted to harassment.
"If the Iranian government was to attempt to coercively obtain this information from journalists and activists of foreign nations, human rights groups around the world would speak out," he said in a statement.
It was not immediately clear how the requested data would be useful to investigators, but Twitter's logs could reveal the Internet addresses that Assange and WikiLeaks supporters have been using, which could help track their locations as they had traveled the world.
The information also might identify others with official access to WikiLeaks' account on Twitter who so far have escaped scrutiny.
U.S. officials have been examining possible charges against Wikileaks for the release of classified documents.
The Associated Press contributed to this report.