The Vancouver Police Department says the incident happened Sunday at 4:30 p.m. PT, when the two girls were playing on a field adjacent to Strathcona Elementary School.
The girls allegedly got into an argument with the man over the ownership of one of their backpacks.
"The argument escalated to the point that both of the girls were allegedly assaulted by the man," the department said in a news release.
The girls ran home and police were called, but the suspect — described as a heavy-built Cantonese-speaking man in his 40s — could not be found.
On Tuesday, police said officers made an arrest in the case.
"The man was identified earlier today after police received tips from the community, and he was subsequently arrested without incident," spokeswoman Laurel Kennedy said in a written statement.
No charges have yet been laid.