Passenger Kris Goodman, 30, was travelling on the bus with his five-year-old daughter when the incident happened at about 20:30 on Monday.
He said two teenagers, one armed with a machete more than a foot long, targeted the bus in Alexandra Parade.
Other vehicles were also said to have been targeted.
Several police vehicles and a helicopter were seen in neighbouring Roystonhill following the incident.
A Police Scotland spokesman said two men were arrested on Monday night.
Two men have been arrested in connection with reports that a teenager armed with a machete attacked a bus in the east end of Glasgow.