The offence took place at the Regent pub in Chapel Allerton as staff were closing up at about 11.40pm last night.
Three masked men kicked open a fire exit door from the beer garden.
A male staff member had been checking the door at the time and was struck in the face, causing a small cut to his forehead.
The men - one armed with a samurai sword and the others with knives - threatened him and a female staff member and demanded money.
The culprits took cash from the safes and also stole a Macmillan cancer charity box before leaving the pub.
The man with the sword was described as 6ft 3ins tall and well built, and the two others were about 5ft 5-6ins tall. Although the men were all masked, one of the shorter two was described as black and another as having dark coloured skin around the eyeholes of his balaclava.
Detective Inspector Phil Jackson, of Leeds District CID, said: “This was a really frightening experience for the victims who were confronted by these masked men armed with weapons.
“They were put in genuine fear when they were threatened and forced to hand over money from the safes.
“We are carrying out extensive enquiries into this incident and would like to hear from anyone who witnessed anything suspicious in the area of the pub in the time leading up to the robbery or who saw the men leaving the scene.”
Anyone with information is asked to contact Leeds District CID via 101 quoting crime reference 13180629648 or call the independent charity Crimestoppers anonymously on 0800 555 111.