The singer said the driver labelled him a “poofter” during the altercation in west London.
The incident is said to have taken place in Fulham at 12.25pm on December 12, the BBC reports.
Speaking on social media after the incident, Mr Young said: “To be called a poofter isn't the nicest thing and it reminds me what a vile thing prejudicial language is to try and shame others."
“I can take action, many young people can't,” he added.
Chief executive of TfL Steve Burton apologised to Mr Young and said everyone should be able to travel “without fear of abuse”.
He said: "We're very sorry to hear of Will Young's experience and are looking into it urgently.
"Everyone has the right to travel without fear of abuse or intimidation and if anyone witnesses or is victim to hate crime they should report it immediately."
He added: "We work closely with our police partners to eradicate hate crimes and fully investigate all reported incidents."
On Friday (January 5), Mr Young said TfL had been “amazing” since he reported the altercation.
He added: “All I need is an apology - no witch hunt .”
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