The Commonwealth War Graves Commission (CWGC) said it was "saddened" by the damage at Harehills Cemetery.
Recently laid turf was ripped up and thrown at the Cross of Sacrifice and a wall bearing the names of the war dead.
However, no graves were damaged or disturbed during the vandalism, believed to have taken place on Tuesday.
James King, from the CWGC, said: "At a time when everyone is concentrating on doing their bit to control the spread of coronavirus, it beggars belief that someone would cause wanton damage to a cemetery like this."
The CWGC is currently in discussions with contractors about how to carry out repairs amid current restrictions on movement.
I hope they catch who did it and put them in the stocks for a day ... feel free to throw what you want at them!