Just before the robbery, the woman was pushing the stroller on the south side of West Las Positas Boulevard, west of Santa Rita Road, police said.
As she walked behind a sound wall into the Las Positas Garden Townhomes around 6:20 p.m., she noticed two men following her, according to police.
Suddenly, one of them pushed the woman to the ground and grabbed her purse from her shoulder, police said.
When the woman fell, the second man took the stroller and started pushing it through the townhome complex but then lost control of the stroller and it tipped over, police said.
The man tried to pull the infant from the stroller but wasn't able to.
The two men then ran east through the complex toward Santa Rita Road with the victim's purse, according to police.
As of this morning, the pair remained at large, police said.
The suspects were described as black men between 18 and 25 years old. They were both clean-shaven with medium builds.
The first man was about 6 feet tall and was wearing a black baseball cap, a black hooded sweatshirt and black pants, police said. The second suspect was about 5 feet 8 inches tall and was dressed similarly.
The woman and her baby were not injured.
Anyone with information is asked to call Pleasanton police at (925) 931-5100.