Four others cleaners, working at a road island near Phan Fah Bridge in the district, were also wounded in the blast, which occurred at about 11am.
The two suffered shrapnel wounds to their faces and legs. They are now receiving treatment at Charoenkrung Pracharat Bridge.
A police commander, Pol Maj Gen Wallop Prathummuang said one of them might have touched one of two ping-pong bombs with their broom, causing it to explode.
The site was a used as a rally site of the anti-government campaigns.