The suspect was described by police as a black man in his early 20s, standing about 6-feet tall and in dark clothes. He pointed a small gun at her and demanded her wallet, police said.
When she protested that she wasn't carrying anything, he left, climbing into the passenger side of a dark van that then took off down the street.
Thirty minutes earlier, police reported, a man in his 50s walking a dog along the 200 block of Walter Hays Drive in Palo Alto also encountered an armed robber.
The suspect beamed a flashlight into the victim's eyes while brandishing a gun. At the robber's command, the man emptied his pockets and then watched the suspect flee with the stolen items.
Witnesses reported hearing a vehicle leaving at a high rate of speed, police said.
Menlo Park police spokeswoman Nicole Acker said the descriptions of the suspect were similar, but the Menlo Park victim was unable to provide more detail.
Detectives from both agencies are investigating the crimes. Police suggest that people remain aware of their surroundings when out for walks, and report suspicious behavior immediately to 911.
Anyone having information about these robberies may contact the Menlo Park Police Department at 330-6300 or the anonymous tip line at 330-6395.