A missing Gracemere woman had facial injuries when the car she was in failed to stop for police at Rockhampton on Christmas Eve, police have said. 

Police have made an urgent appeal for information about 32-year-old Krystal Phillips, who is believed to be with 33-year-old Gracemere man, Jaydon Leahy, in a blue Holden Trax station wagon.

Detective Acting Senior Sergeant Jason Milner said the pair had been in a relationship for some months. 

He said Ms Phillips had not contacted family on Christmas Day, including her 11-year-old son. 

"The behaviour is concerning at this time which is why we want to locate Krystal, just to check on her welfare," he said. 

"The fact that she has facial injuries, and the fact that she hasn’t contact anyone, that is concerning for us."

The car failed to stop for police at 8:15pm on Saturday, December 24 at Cobraball, and was then seen Christmas morning at a Gympie petrol station, and again on the Warrego Oakey Highway that afternoon. 

On Monday morning, it was seen at Miles, westbound on the Warrego Highway. 

Detective Acting Senior Sergeant Milner said it was "concerning" the car did not stop for police. 

"If they see the vehicle, please contact police immediately on triple-0 … do not approach the vehicle."

The car's registration is 050-CN5.