The Singapore Civil Defence Force (SCDF) said the injured passengers were taken to hospital, with most sustaining minor injuries.
Transport officials said a moving train collided with a stationary faulty train at the elevated Joo Koon station in the far west of the city state.
"At 8.19am, a second train stopped behind the first faulty train. At 8.20am, the second train moved forward unexpectedly, and came into contact with the first train," regulator Land Transport Authority (LTA) and train operator SMRT said in a joint statement.
It added that 23 passengers and two SMRT employees "sustained light to moderate injuries" and have been sent to nearby hospitals.
Both LTA and SMRT are investigating the incident, the statement said.
Densely populated Singapore's metro system has been hit by repeated delays and breakdowns in recent years, generating public anger in a financial centre in which the cost of car ownership is among the highest in the world.