The 55-year-old victim answered the door of his home in Wallace Court, Prestwick, to a woman at about 16:30 on Sunday.
As they spoke, a man pushed his way into the house, attacked the wheelchair user with a knife and demanded money.
The couple stole more than Â£1,000 before escaping. Detectives believe it was a targeted attack.
The victim was taken to Ayr Hospital for treatment to a neck injury. His condition was described as "stable".
The suspects are both white and in their early 40s. The man was about 5ft 10in tall, slim and was wearing a blue beanie hat, jeans and a blue fleece.
The woman was between 5ft 6in and 5ft 8in tall, slim and had long, dark hair. She was wearing a dark jacket which may have had white writing on the back.
Det Insp Alan Sommerville said: "Thankfully the man was not seriously injured during the attack but it was a terrifying and very nasty experience for him.
"I do believe that he was targeted and would appeal to anyone who recognises the descriptions, who may have seen the couple hanging about either prior to or after the robbery, to contact police."
A wheelchair user has been treated in hospital after being attacked by thieves in his own house.