Alexander Diaz, 36, was taken into custody around 5 a.m. on Wednesday morning.
Fremont police said Diaz stole the van and accelerated into the officer, 43-year-old Patrick Brower, on Monday after Brower spotted the vehicle.
Brower was trapped under the van, which struck a light pole.
The officer was forced to undergo reconstructive surgery to his leg and foot, but he is expected to be released from the hospital this week.
The Associated Press contributed to this report.