When the Connecticut Democrat-turned-independent asked for a routine extension beyond the 10-minute limit allotted him -- Franken, a comedian-turned-Democratic politician who was presiding over the Senate session -- refused, The Washington Post reported.
"In my capacity as the senator from Minnesota, I object," Franken said.
While Lieberman, who has been in the Senate for 20 years, caucuses with the Democrats, he has angered many in the party by rejecting any public healthcare option.
Sen. John McCain, R-Ariz., Lieberman's choice in the 2008 presidential race, objected to Franken's objection.
"I don't know what's happening here in this body, but I think it's wrong," McCain said. "I'll tell you, I have never seen a member denied an extra minute or so, as the chair just did."
Sen. Carl Levin, D-Mich., pointed out to McCain that it had happened before -- earlier in the afternoon when Sen. Mark Begich, D-Alaska, refused to give Sen. John Cornyn, R-Texas, more time.
Lieberman said, just after Franken cut him off, "Don't take it personally" -- advice the Post said appeared to be directed at himself. He later said there were no hard feelings.
Celebrity Families of 2014 [PHOTOS]