Barbara Stensland, 43, from Cardiff, went to Carmarthen on 5 August.
When she tried to get a taxi from the railway station to the venue, less than one mile (1.6km) away, she was refused.
Carmarthenshire council's senior licensing officer, Justin Power, said: "We will investigate this matter and take any necessary steps."
Ms Stensland told BBC Radio Cymru's Post Cyntaf programme it took her more than an hour to reach the venue.
She said: "I went to the first taxi in the queue outside the station, I told him where I wanted to go.
"He laughed. I thought he was just joking along because I knew it was a fairly short distance.
"When I said 'seriously, can I get in the taxi?' He said 'no, I'm not taking you.' So he pointed me helpfully in the right direction and told me to walk."
Urtha Felda, from MS Society Cymru, said: "We have heard of people having trouble getting taxis.
"If somebody's still walking you can't see that they're disabled - if someone's in a wheelchair it's really obvious.
"It's not obvious, so I would say to people - don't make judgements."

US-based golf course designers Mike Keiser, Bill Coore and Todd Warnock have proposed creating the course at Coul Links, near Dornoch.
Four conservation charities have joined forces to oppose the project.
The developers said they were aiming for "minimal intrusion on the landscape".
The Scottish Wildlife Trust, RSPB Scotland, Buglife and Plantlife have concerns the course will result in the loss of a protected sand dunes habitat and rare wildlife.
The developers, who have held two meetings in the local area as part of public consultation on the plans, said the building of the course would involve laying turf over less than 55 acres (22ha) within a Site of Special Scientific Interest (SSSI).
SSSIs are areas indentified as having a diverse range of wildlife and geology.
The developers said their planned new course, close to Embo, would compliment nearby Royal Dornoch golf course and others in the East Sutherland area.
Mr Keiser, who owns Bandon Dunes Golf Resort in Oregon, said: "This is a wonderful opportunity to deliver a spectacular championship links golf course which represents all that is natural about golf, in the home of golf.
"Our golf course developments aim for minimal intrusion on the landscape and the utmost care and respect for the environment.
"Our team of environmental advisors is ensuring complete sensitivity to the land, and its location."

TV coverage showed hundreds of empty seats at Leicester City's third-round replay against Spurs, with many home fans missing the start of the game.
One supporter claimed the delays at the King Power Stadium, caused by ticketing problems, could have "turned nasty".
Leicester City FC has apologised and launched an investigation.
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Joe Walker, a Foxes fan, said he arrived at the ground at about 19:25 GMT and saw "thousands of people attempting to gain access".
He said after 20 minutes in the queue his "print at home" ticket was rejected at the turnstile and he was told to go to the ticket office to get a new one.
"We then walked towards the sub ticket office and as I questioned another steward he just laughed and said: 'You should see the queues for it'."
Mr Walker eventually had a ticket printed at the main office, but described the way staff managed the situation as "a shambles".
"Not one announcement had been made over the loudspeaker system," he said.
"There was no organization or information coming from any of the stewards. It could have easily have turned quite nasty with the sheer amount of people."
Leicester City FC said: "A significant number of supporters experienced difficulty gaining admission to the stadium, resulting in many missing the start of the match.
"The club is currently investigating the cause of Wednesday night's delays as a priority, to ensure any difficulties experienced are not repeated at future home matches."
Leicester lost Wednesday night's match 0-2.
A woman with multiple sclerosis has said she was refused a taxi to a meeting of the MS Society because the journey was too short.
[NEXT_CONCEPT]
The developers of a planned 18-hole championship golf course have sought to allay concerns about their proposal's impact on a protected coastal area.
[NEXT_CONCEPT]
Football supporters have vented their anger after crowds of them were left stranded outside a Premier League stadium during an FA Cup match.