Southwest Airlines has apologised to a woman who claimed a member of staff stopped her from boarding because they did not believe her one-year-old biracial son was hers.

Lindsay Gottlieb claimed in a series of tweets that before a flight from Denver to Oakland, a desk agent asked her to "prove" that her son was hers "despite having his passport".

“She said because we have different last name," the woman's basketball coach from the University of California, Berkeley wrote.

"My guess is because he has a different skin colour."

Ms Gottlieb was travelling with her fiance, Patrick Martin, the boy’s father, who is black.

Airlines are not required to match the last name of a child and guardian for domestic flights.

“We have reached out to Ms Gottlieb directly to address her concerns and will utilise the situation as a coaching opportunity for our Employee,” Southwest said in a statement. We apologise if our interaction made this family uncomfortable — that is never our intention.”

Ms Gottlieb said the encounter was hurtful, but that she appreciated Southwest’s apology.

“I felt that in this situation it was my responsibility to say ‘Hey, this isn’t ok,”’ Ms Gottlieb said.

“I hope the coverage this has received can serve as a learning opportunity and that all families — regardless of how ‘traditional’ they may or may not look — are treated with dignity and respect.”

Ms Gottlieb, Mr Martin and their child were eventually allowed to board.