About 70 graves at Choa Chu Kang Cemetery were damaged by some 200 trees which fell during Friday's thunderstorm.
Some tombstones were split in two, while others were ripped out when trees were uprooted.
The perimeter fences at the Surau building and cemetery office were also damaged by the storm, said the National Environment Agency (NEA) in a statement on Monday.
NEA was first alerted to fallen trees at the Chinese Cemetery (Blocks 7A, 7C, 8, 10, 15, 16), Muslim Cemetery (Blocks N-1-1 and N-1-2) and the Christian Cemetery (Block 1) at about 4pm last Friday.
No injuries were reported.
"We are informing the next of kin of the affected graves so that they can proceed to engage their own contractors for repair works," said NEA.
Approximate number of trees that were felled during last Friday's thunderstorm
Wind speed hit a high of 133.3kmh in Tengah at 3.50pm that day, said the Meteorological Service Singapore last Saturday.
Ms Zubaidah Mudin, 42, was on her way to the Muslim Cemetery on Sunday morning to pay her respects to her late grandparents when she was greeted by the disconcerting sight.
"You could see some trees had fallen over the tombs, with their roots sticking out. There was one where the tree had smashed into the tiles." The damaged graves were in the older plots, which have more trees lining the perimeter, said the communications specialist.
Her grandparents' graves were not affected by the destruction as they are in the newer plots.
Said Ms Zubaidah: "I felt sympathy for those whose relatives' graves were affected because it's a place of rest. And you see it so... disturbed all of a sudden."