The woman, believed to be in her 30s, was struck near 16 Avenue and 17 Street N.W. at 11 a.m.
Sgt. Colin Foster said the woman worked at the Centex gas station and followed the truck into the nearby Home Depot parking lot after the driver didn't pay for gas.
"It appears then that the gas station attendant somehow managed to get onto the hood of the vehicle as the vehicle started to drive away," Foster said. "During the course of that dynamic, the pedestrian now fell off the vehicle and the vehicle drove over her before fleeing from the scene."
Police are looking for a brown Ford F350 with licence plate EUX 378.
"Paramedics took her to Foothills Hospital in serious, potentially life-threatening condition with multiple traumatic injuries including potential head injuries. There were no other people injured at the scene," EMS spokesman Stuart Brideaux said in a press release.
Police are gathering video surveillance to try to confirm the description of the vehicle involved.