A man who uses a wheelchair said he pulled himself up three flights of stairs to take his driving theory test as the centre had no disabled access.
Sam Law, 21, from Cardigan, Ceredigion, said the experience left him feeling angry and "completely left out".
His mother took photos of what happened at the centre in Haverfordwest, Pembrokeshire on Thursday.
The Driver and Vehicle Standards Agency (DVSA) said it was "extremely sorry for the unacceptable distress".
A spokesman said it was investigating as a matter of urgency, adding: "We want everyone who is able, to take any driving test and will always make reasonable adjustments for people who are disabled and want to pass their theory or practical exam."
Service providers have to make reasonable adjustments for people who have a disability so they are not put at a substantial disadvantage compared to those who are not disabled when accessing services.
Mr Law said he specified he used a wheelchair when he booked his test online and requested to have it in Aberystwyth as he knew the centre there had wheelchair access.
He said he tried calling the Haverfordwest centre on the morning of the test to check access but no-one picked up.
"I was very disappointed and angry," he said.
"I felt left out, completely left out."
He said staff at the centre advised he return home and book another test, but he did not want to delay the test so decided to climb the steps with his brother's assistance.
"It was very, very hard work - lifting yourself. Because I sit down all the time, I break bones easily," he said.
Mr Law, who has used a wheelchair since having a spinal stroke when he was 16, said he was shocked a building used by a government department did not have disabled access.
"It shouldn't be a case of 'you need to go to another centre'," he said.