The customer was told she was unable to get on a Featherstone to Leeds train because her mobility vehicle didn't fold.
The incident was brought to light at a full council meeting by Labour member Graham Isherwood, who took up the lady's case.
Northern confirmed its policy currently prevents unfoldable scooters being brought onto a train because "there isn't space". It said that the situation would be reviewed when it starts using a new fleet of carriages in the years to come.
But Coun Isherwood said the situation was "appalling" and called for the government to step in.
"The way Northern treats disabled passengers is absolutely shocking," he said.
"This elderly lady came to see me at my surgery on her scooter.
"For years, her only joy was being taken to Leeds by a friend once a month. They'd have a tootle round Leeds, and then come back on the train and come home again. But now she can't.
"If it's a wheelchair that's fine, but if a disabled person using a little shopper-type scooter and they can't fold it up themselves, they're not allowed on.
"I thought, "This can't be a policy," so I checked up with Northern, and it turns out, yes it is."
Coun Isherwood said he had written one of the under-fire company's new directors to complain about the situation, to be told that the policy may only be changed when Northern starts using more modern carriages in 2021.
He added: "It's an absolute disgrace.
"I'm hoping we can get some support to change this. It's 2019, not 1919.
"Surely the government should be looking after our most vulnerable people."
In response, a spokesman for Northern said: "At the moment, the only mobility scooters we can take on our trains are those that can be folded and carried on as a piece of luggage.
"This is due to the restricted manoeuvrability and stability of mobility scooters and the design of our current trains. Most of our trains were built before mobility scooters were introduced and so were not designed with them in mind.
"Our train crews are happy to assist with loading and unloading a folded scooter. We participate in the industry-wide Passenger Assist programme and encourage customers who may require assistance when travelling on our services, to contact us before they travel on 0800 138 5560 to see how we can help.
"As we continue to work to upgrade our train fleet, we are focused on improving access for all."
Strike action will disrupt Northern services again this Saturday, having taken place every weekend since last September.