There were no injuries, the campaign said.
Live television footage showed Pence standing in the rain near the plane among emergency vehicles, talking to police and other officials.
“Governor Pence and everyone on board the plane is fine,” said Marc Lotter, Press Secretary for Donald Trump for President 2016, the reporters on the runway.
“There were no injuries. The Governor is obviously heading to end the evening and he will be back on the campaign trail tomorrow.”
Republican presidential nominee Donald Trump called Pence to check on him after the incident, the campaign said.
“Mr. Trump did reach out to Gov. Pence. He’s glad that everyone on board is safe,” Trump spokeswoman Stephanie Grisham said in an emailed statement.
Trump called him from his motorcade while en route to a rally in Geneva, Ohio.
There were about 30 people onboard the plane, including Pence’s wife, Karen, and daughter Charlotte, MSNBC said.
The plane was coming from Fort Dodge, Iowa, where Pence had participated in a campaign event. The takeoff from Iowa was delayed for about two hours because of bad weather in New York.
Pence has canceled his appearance at a fundraiser scheduled for Thursday night at Trump Tower in Manhattan, MSNBC reported.
(c) Copyright Thomson Reuters 2016