The sheets, extending across three traffic lanes, were placed to cover the part of the road that had been dug up for an underground power line laying project.
The driver of the truck, which was carrying soil from a construction site and ended up with its rear stuck in the hole, reportedly told police his vehicle had not exceeded the weight limit.
The two injured, meanwhile, were motorcyclists who crashed when the road collapsed.
Police were advising motorists to avoid the area while they try to pull the truck out. Traffic was backed up for several kilometres as of press time.
Bangkok governor Chadchart Sittipunt arrived at the scene at around 1pm, and ordered an immediate halt to the power line project underneath until the cause has been found and the road fixed.
This is the second accident to be caused by sinkholes on Bangkok roads this week.
On Monday night, a Toyota Fortuner fell into a hole on Chaturathit Road near the Si Ayutthaya intersection in Ratchathewi district.
Luckily, only the front half of the vehicle had fallen into the opening and the SUV and its driver could be pulled up by a crane. Nobody was injured in this accident.
Police said the 1.5-metre-wide, 6m-long and 8m-deep hole had been covered by a concrete sheet, which collapsed under the vehicle’s weight. The hole is part of the city’s project to construct underground cesspits leading to Makkasan Swamp.