About an hour and a half after the incident, one of LaGuardia's two runways reopened for arriving and departing flights. The Federal Aviation Administration said the airport's other runway will remain closed indefinitely pending clearing of the aircraft.
According to the FAA, there were no injuries among the 48 people -- 37 passengers and 11 crew -- on board the Boeing 737, which was arriving from Fort Dodge, Iowa.
Pence tweeted, "So thankful everyone on our plane is safe. Grateful for our first responders & the concern & prayers of so many. Back on the trail tomorrow!"
The plane made a rough impact when it landed, according to The Associated Press, which also reported that the pilot slammed on the brakes and passengers could smell burning rubber.
After the incident, which happened at 7:41 p.m., Pence headed to a New York City hotel.
"Governor Pence and everyone on board the plane is fine," said a Pence spokesperson. "Thankfully some great work by the Port Authority and all the airport authorities, the dedicated flight attendants, there were no injuries. The governor is obviously heading to end the evening and he'll be back out on the campaign trail tomorrow."
Passengers, including Pence, were evacuated through the back of the plane.
The FAA said the plane was resting against the perimeter fence after it skid of the runway. The FDNY responded to the scene.
Two officials from the Port Authority of New York and New Jersey -- which manages LaGuardia -- told ABC News that the aircraft was stopped from going onto the adjacent highway by the crushed concrete "arrestor bed" at the end of the runway. The arrestor bed is designed to do precisely what it did.
A senior federal official told ABC News that nothing unusual had been reported to the air traffic control tower regarding the flight or the aircraft prior to tonight’s incident with the plane.
The National Transportation Safety Board is sending a team to investigate the incident.
At a rally in Ohio Thursday night, Trump told supporters, "I just spoke to our future vice president and he's OK. He was in a big accident with a plane. The plane skidded off the runway and was pretty close to grave, grave danger. ... He's fine, he got out, everybody's fine, everybody's fine."
And Trump's rival, Democratic presidential candidate Hillary Clinton tweeted, "Glad to hear @mike_pence, his staff, Secret Service, and the crew are all safe. -H"
Editor's note: This story has been updated to reflect that there were 48 people on board the plane -- 37 passengers and 11 crew.
ABC News' Ines DeLaCuetara, Candace Smith, Aaron Katersky, Josh Margolin, John Santucci, Christopher Donato, Whitney Lloyd, Benjamin Stein, Darren Reynolds and Erin Dooley contributed to this report.