At least three headstones were damaged at Marton Burial Ground after the car had driven into them at around midday on Sunday.
The 32-year-old woman from Lancaster was arrested at the cemetery for numerous offences.
Residents have spoken of their shock about the incident.
Norma Smith, 73, of Preston Old Road said: “It was unbelievable the amount of police cars that turned up.
“I can’t believe someone has even attempted to drive onto the cemetery, the roads are that small.
“I feel sorry for the families who have had their relatives gravestone destroyed. I would feel sick if that happened to my parents headstones.”
Ron Jamieson, 65, lives on Birch Tree Gardens which backs onto the cemetery and saw the woman get arrested.
He said: “I don’t quite know what was going through her head when she drove up there.
“It must be very upsetting finding out one of your relatives’ graves has been driven into by a car.”
The damaged Vauxhall was later recovered from the cemetery however damaged parts still littered the graves yesterday.
A Blackpool Police spokesman said: “We responded to calls at 12.10pm on the Sunday to a road related offence at Marton Burial Ground.
“Officers discovered the car had damaged a number of headstones in the churchyard and they arrested the female driver at the scene for a number of offences.”
The woman was arrested on suspicion of dangerous driving, possession of class B or C drugs, driving whilst disqualified, driving with no insurance and drug driving. She remained in custody yesterday evening
A spokesman from the Diocese of Blackburn, which oversees the cemetery, said the families of the damaged gravestones will be contacted.
They said: “If there has been damage to headstones, they are not the property of the church but the family of whose grave it is.
“There is a process we follow in this sort of circumstance where we contact the families and liaise with them about the damaged headstones.”
No one was available for comment from St Paul’s Church, which is the church connected to the cemetery.