The 53-year-old Republican submitted his resignation after the World-Herald reported he had made about 2,000 calls to four women in the past four years on his state-issued cellphone. The newspaper said many of the calls were lengthy and took place late at night.
Gov. Dave Heineman, who revealed Sheehy's resignation at a news conference, said it left him with "a knot in my stomach" and "deeply disappointed."
"He's done a lot of good things for the state, but that trust was broken, and he's resigned," Heineman said.
The governor the process for filling the post would begin Monday.
Sheehy, a former mayor of Hastings who became lieutenant governor in 2005, had had his eyes on the governor's seat, filing paperwork to enter the 2014 race in December 2011. A year later, his wife of 28 years Colleen filed for divorce and that was followed by this week's revelation, the newspaper said.
"I doubt he will continue his campaign for governor, and no, I would not support him under the circumstances," said Heineman, who declined to discuss details of the conversation he had with Sheehy after learning of the matter Friday.
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Beyonce flaunts bikini body, Blue Ivy in vacation pics