According to police, the attack happened on 43rd Street near Avenue Q around 8:30 a.m.
Police said the man came out of nowhere.
"A male approached one of the women, pushed her down and then it looked like he may have been touching himself in a gratifying manner before he fled," said Captain Joshua Schirard with the Galveston Police Department.
Police say what's especially disturbing is that this is a stranger-on-stranger crime.
Oftentimes, victims know their attacker but not in this case.
The woman's daughter says her mother already had a broken hand so she wasn't able to defend herself.
The woman suffered scratches but is okay. Now, neighbors are on heightened alert.
"Hopefully they can find him because next time he may do something else," said Shirley Danesi, a neighbor.
Police say to never walk alone and be aware of your surroundings.
Shirard also says if someone approaches you, talk to them. It could catch them by surprise and throw them off.
"If you confront them, by confronting I mean, by looking at them, by looking at them and addressing them, you know, good afternoon, good morning," said Shirard.
There is only a vague suspect description. If you know anything, you're asked to call the Galveston County Police Department.