Paula and Chris King said their 20-year-old son Ryan was having a meal at Zizzi in Manchester's Trafford Centre on Monday 4 April with his two carers Sharon Farrington and Faizal Shah.
Ryan and his carers had chatted to a man with his two children sat at the table next to them during the meal.
"Later on when we asked for the bill, the waiter just came up and and said the family next to us had sorted it," Shah, 31, told Manchester Evening News.
"Honestly, words cannot describe how I felt. Ryan was really happy."
Shah said before the unknown man left, he said to them: "It’s been lovely to meet you - enjoy the rest of your day".
However he made no mention that he had paid their £20 bill before leaving the restaurant.
Shah said Ryan, who cannot walk or talk, understood how generous the stranger had been and was really happy when they told him.
Ryan's mum, Paula King, 49, wanted to find the man and thank him for his generosity.
So she posted the exchange on Facebook to see if someone could help her locate him.
"It was a really, really nice thing to do," King said.
"Ryan’s got a smile that would light up any room. We’re just so grateful that someone would do that and make him so happy like that."
King's Facebook status read: "Can I ask all of our friends to please share this post. Today Ryan went to the Trafford Centre with his carers Sharon Farrington and Faizal Shah.
"He dined in Zizzi and a family of four were on the next table, they got talking to Ryan’s carers because there was a delay in service.
"When the family were going the gentleman came over and said: 'Nice to meet you and enjoy the rest of the day’ and off they went.
"The waiter came over around 10 minutes after to say the family had paid for Ryan’s meal.
"I would just to like to say a big thank you for doing something so kind for Ryan and a massive thank you from Ryan."
She has not yet been able to get in touch with the stranger who paid the bill.
At the beginning of the year, another mum publicly thanked a stranger for their random act of kindness during a lunch trip.
Lauren Copp Nordberg, 35, from Washington, America, was out with her six-year-old son Elliot who has Asperger syndrome.
A stranger paid for her bill and left a note saying: "Have a great day. You are doing a wonderful job. God bless. From a mother who knows."