The kidnapping was reported at about 1 a.m. Sunday.
The 19-year-old victim was walking near the intersection of 19th and Mission streets when a man approached, threatened to shoot her and dragged her to the nearby van, according to police.
The suspect, described as a man in his mid 20s, tried to make the woman swallow a pill and shoved her into the back of the van before driving off, police said.
However, after the van had traveled about a mile, the woman managed to open one of the doors and flee when it stopped at the intersection of 17th and Kansas streets in Potrero Hill, according to police.
The man fled in the van, and had not been found as of today, police said.
The woman was not injured.
Anyone with information about the case is encouraged to call the Police Department's anonymous tip line at (415) 575-4444 or send a tip by text message to TIP411.