The company confirmed an incident involving two 22-year-old students from Slough, Berkshire took place on a No. 7 bus at Russell Square on Tuesday.
The firm said the women had made a complaint to Transport for London (TfL) and that Metroline was following it up, but stressed it was still merely an allegation at this stage.
Interviewed by the BBC, Yasmin, who was wearing a hijab, which leaves the face and hands uncovered, and Atoofa, dressed in a niqab which covers the face but leaves the area around the eyes open, said they were stopped from boarding because of their appearance.
"He (the bus driver) said, 'I am not going to take you on the bus because you two are a threat,'" Yasmin said.
A Metroline spokesman told Reuters: "We take this very seriously and will make a thorough investigation into the allegations as a matter of urgency.
"However, Metroline can unequivocally state that such views would not be representative of the company in any way and that we are committed to respecting equality and diversity for all."
He said the company was still trying to establish the facts and had narrowed the incident down to three drivers who were being interviewed.
"If it is the case that one of our drivers off his own back refused entry to someone for that reason then that, obviously, is unacceptable," he added.
The Muslim Council of Britain said it was "deeply concerned", but could not comment on individual cases.
Metroline operates the service on behalf of Transport for London (TfL.)
