The incident took place just after midday on Thursday, when a Great Northern train arriving at Platform 11 from Cambridge overshot its resting position.
Emergency services rushed to the scene to tend to five passengers on board who sustained "minor injuries", Network Rail confirmed, but paramedics delivered two people to hospital.
Some evening services were cancelled as a result and a two doing the same route will run with fewer carriages than normal later tonight.
One passenger described the event, saying there had been a "huge bang" and everyone had been "thrown around".
An independent examination team, the Rail Accident Investigation Branch, has been notified and is expected to carry out a full review of the incident shortly.
Great Northern’s passenger service director Keith Jipps told The Huffington Post: “We worked with paramedics to help those who were injured and apologise to those affected by the incident. We will cooperate fully with any investigation.”
A Network Rail spokesperson said the train had been involved in a "low-speed collision".
“A train arriving at London King’s Cross from Cambridge has been involved in a low-speed collision with the buffer stops as it arrived into platform 11," they said.
"There were no reports of any serious injuries, however emergency services assisted a small number of passengers who required medical attention.”