Thea says although her husband, 27, was calm about the situation, she complained to Uber - and received an "impersonal" response.
An Uber spokesperson told Mirror Online the firm "does not tolerate any form of discrimination from riders or licensed drivers".
They added that the driver says he waited for Thea and Jeremiah to exit the station but "eventually had to cancel the trip as he was causing an obstruction".
However, Thea said: "It seems obvious to me that he was very racist.
"There really could be no other explanation for why he would just drive off like that.
"I requested an Uber as soon as we got off the coach and he gave me a call straight away to find out where I was.
"When I came outside and he spotted me, he was really nice to me [as he remained on the phone] - very lovely. There was no problem.
"My husband had all the suitcases and was lagging behind me, but he eventually came out and handed me one of them.
"He sounded completely nice on the phone but it was when he saw my husband.
"[Jeremiah] is a tall black man. I don't know if the driver felt threatened.
"My husband works with elderly people and a team leader at a care home. He's the sweetest, most gentle person ever.
"I don't understand how we can allow these racist stereotypes to be perpetuated.
"When you are a biracial couple you see a lot of people who still have a problem, but it's still one of those things you don't expect to see in modern-day England."
The couple, from Leicester, were in a rush to get to the airport after the minicab driver allegedly drove off without them.
They ended up ordering another car via the app.
Thea said: "The next minicab was also an Uber.
"The driver didn't seem very surprised when we told him what happened.
"The new driver was a young Arabic man and he seemed unfazed by it.
"I'm just really disgusted. It's so messed up but Jeremiah is just used to it. We're both utterly baffled.
"We live in Leicester and it's a very multicultural community - I'm not sure what Manchester is like but I wouldn't have expected this to happen."
When Thea contacted Uber to complain about her experience, she claims she received a standard 'impersonal' response.
Thea said: "Uber sent a reply to my complaint which was really impersonal and you can see that they haven't actually read it properly.
"It said: 'thank you for your advice. We will take this into consideration when we are doing our next recruiting'.
"After that, they have messaged me saying that basically, because of driver security, they cannot disclose what will happen but they are going to investigate.
"I asked them when it is concluded, if will they let me know what happens but they said they can't do that either.
"They said the minicab driver was suspended whilst they carried out the investigation.
"I really want for Uber and the driver to take responsibility and would really like people be more aware that their actions have consequences and society needs to change."
A spokesperson for Uber told Mirror Online: "Uber does not tolerate any form of discrimination from riders or licensed drivers who our the app.
"We have spoken to this licensed driver who strongly denies these claims.
"He has told us that he waited for the passengers to exit the station but eventually had to cancel the trip as he was causing an obstruction."