Shropshire Council workers were called to the Queen Street car park at about 8.30am yesterday.
Jason Hughes, street lighting and traffic signals commissioner for Shropshire Council, said the damage was caused by a Veolia bin lorry.
The damaged light has now been removed from the car park.
Mr Hughes said: "We were made aware of this incident yesterday morning where a lighting column had been knocked down in the Queen Street car park. The damage was caused by a Veolia bin lorry."
He added: "The column was made safe yesterday morning and now has been removed from site.
"Veolia have already admitted liability for the damage and a claim has been logged with their insurance company.
"We will now instruct our contractor to replace the column in due course."
Residents living nearby said they heard the street light fall to the ground.
Richard Sharpe, who lives near to the car park, said: "I heard it fall and it was lucky that the light didn't hit any vehicles because it would have caused quite a lot of damage."