The woman has been ID'd as 35-year-old Daly City resident Christine Svanemyr.
The incident happened just after 2 p.m. Thursday at Holly Park in the city's Bernal Heights District.
It is a very tight knit community, so people in the neighborhood were shocked and saddened to hear that a woman was hit and killed. By Thursday evening, a memorial of flowers had been set up at the park where she was struck.
A witness tells ABC7 News that the truck was driving across the grass, which was very busy at the time, and then ran over Svanemyr who was sunbathing with her child and dog nearby.
Svanemyr was transported to San Francisco General Hospital with life-threatening injuries where she later died. The child and dog were not hurt.
The driver of a green Parks Department vehicle took off after the incident but was later found and detained by police at Crescent and Agnon avenues. The driver has been arrested on suspicion of felony hit and run.
Neighbors say that parks vehicles are always here and it's a big problem with people driving on the grass.
"Bound to happen, I'm surprised that we haven't had more dogs run over because some people let their dogs run loose," neighbor Patricia Leach said.
Leach has lived here since the 1950s and says it's a huge problem. She hopes there will be some sort of policy change in the future because the park is way too busy to have vehicles driving on it.
Supervisor David Campos said he was not aware of the concern but promises a thorough investigation.
"At the end of the day we want to make sure that our citizens are safe and that they can enjoy parks and rec space in a safe manner," he said.