Both the 8.03am service from King's Cross to Leeds and the 09.06am King's Cross to York services have been cancelled so far, with warnings that other services may be subject to delays or amendments.
The 10.02am service from York to King's Cross has also been cancelled due to the incident.
In a tweet, LNER said: "It is with deep sadness that we report a person being hit by a train between Peterborough and King's Cross.
"Services will be delayed in the area and alterations may occur."
Meanwhile, the 07.15am Leeds to King's Cross service was cancelled due to a fault.