The 42-unit complex started to burn just before 8:30 p.m. at 184 Callan St. in unit No. 210 where heavy smoke prompted the woman to knock out the window and scream for help, fire spokeswoman Aisha Knowles said.
A neighbor of the unit, Mark Montoya, had evacuated the building but went back in to his next-door unit to retrieve a blanket to catch the woman, Knowles said.
Montoya, San Leandro High School student Mario Sanchez and two other neighbors reportedly held the corners of the blanket and encouraged the woman to make the 18-foot leap from her window.
The two other neighbors apparently left before firefighters were able to make note of their names.
Firefighters contained the fire within 20 minutes of arrival, and kept it confined to the single unit, Knowles said.
Two other residents of the building, Lincoln Taukave and Tyari Washington, were using the existing house hose lines on the second floor to help knock the flames down, she said.
However 15 occupants were displaced because their apartments were damaged by the smoke and water, she said.
Fire officials believe the fire may have started in the kitchen, from deep-frying on the stovetop and caused about $500,000 in damage.
The older brother of the woman who jumped was also able to safely evacuate.
No injuries were reported.