Mohammed Matlub Mir, 69, was working alone in the convenience store near Cross Flatts Park on Beeston Road when the men burst in and ordered him to give them the contents of the till.
All of the men were armed with large knives or machetes.
Mr Mir did not put up a fight but during the course of the incident – which happened at about 7pm yesterday and lasted two or three minutes – one of the raiders cruelly lashed out at his hand with his machete.
The stunned dad-of-four and grandfather-of-seven only realised he was bleeding after the men fled the store with its takings.
Left in a state of shock, he tried to stem the flow of blood from the “deep cut” with tissues as paramedics and police made their way to the scene.
He was then taken to Leeds General Infirmary, where he received treatment for the injury before being released.
Recovering at his home in Beeston today, Mr Mir was not feeling well enough to talk about the incident, which was captured on CCTV.
But, speaking to the Yorkshire Evening Post, his daughter, Sadia Mir, 40, hailed him as “very brave” for the way he had responded to the scare.
She said: “He is very shaken up, of course, it’s kind of still hitting him.
“But he’s also quite insistent that he wants to go back to work at the shop when he’s well enough.
“We know it could have been a lot worse. When you look at the CCTV footage and see the size of the knives and machetes then you just think he was very, very lucky.
“We are all proud of how he reacted – he did not try to struggle with the men and that was the right thing to do.
“If he had tried to put up a fight then the attack on him could have been much more serious.”
Police have issued an appeal for witnesses or other people with information about the robbery to come forward.
Leeds District CID’s Det Insp Richard Holmes said: “This was obviously a very frightening experience for the victim and we are carrying out extensive enquiries to identify those involved.”
Anyone with information is asked to ring Leeds District CID on 101, quoting log reference 13180154808, or Crimestoppers anonymously on 0800 555111.