Standard Parking Inc. said it respects the equal rights of all customers and doesn't tolerate discrimination of any kind. It also said the employee was suspended after the company learned in July of the late June incident.
According to a police report, one of the men involved said they had been holding hands and that the driver ordered them to the back when one of them started to sing.
The city's Human Rights Office will look into the incident, the Albuquerque Journal reported.
Mayor Richard Berry said he believed the driver behaved inappropriately.
"We're out there aggressively making sure this never happens again because this does not belong in Albuquerque, New Mexico," Berry told KOB-TV. "This does not reflect Albuquerque, New Mexico, and as the mayor I'm upset about it, and we want to make sure we get to the bottom of it."
The incident comes as the New Mexico Supreme Court considers a case involving an Albuquerque photography business whose owner declined to shoot the commitment ceremony of a lesbian couple.
The couple alleged discrimination. Their attorney argued the business openly advertises its wedding photography services, and as a public business is required to follow the same anti-discrimination laws as any other company.
An attorney for owner Elaine Huguenin said gay marriage is against his client's religious beliefs, and she was exercising her rights to free speech and artistic freedom.
It's unclear when the high court will rule.