Paterno, a son of the late Penn State football coach Joe Paterno, said he concluded that trying to overcome a challenge to his nomination petitions would be a long process that would distract from the campaign.
"I do not want an ongoing legal back and forth to be a distraction in this race," Paterno said in a statement. "The outcome of this election is too important for the future of the working families and all the people of this commonwealth."
Paterno was one of six candidates vying to be the running mate of whoever is picked as the Democratic gubernatorial nominee. Republican Gov. Tom Corbett has a longshot challenger who also faces a legal challenge to his nomination petitions.
It remained unclear whether Paterno's name would remain on the statewide ballot, potentially drawing votes away from the active candidates, since the deadline to withdraw from the ballot passed Wednesday.
Paterno can petition the court to take his name off the ballot, but if he doesn't, the candidate who challenged Paterno's petition said he will pursue his legal options to make sure that happens.
"We've always said this was an issue about the rules set out by the commonwealth," said Brad Koplinski, a Harrisburg city councilman. "I believe Jay Paterno would have added a lot of good discussion to this race, such as his thoughts on education. I hope that he will be a voice in Democratic politics for many years to come."
Paterno has been active in Democratic Party politics and worked as an assistant football coach under his father through 2011. The elder Paterno died in January 2012.
Like other candidates for lieutenant governor, Paterno needed to collect at least 1,000 voters' signatures, including at least 100 in each of five counties.
Koplinski's lawyer, Lawrence Otter, said Paterno collected a total of 1,117 signatures. He said the numbers of signatures in three counties - Philadelphia, Chester and Mifflin - fell below the 100-signature threshold after a review disqualified many signers for reasons that included not being registered as Democrats and not being registered in the county.