It was trapped for five hours after turning from Terrace Road into Rose Hill at about 04:00 GMT on Tuesday.
A legally parked car was eventually moved to end the blockage but the lorry became stuck again on a turn and had to wait while another car was moved.
Tesco said it “apologised for any inconvenience caused.”
A spokesman added: “One of our vehicles got into difficulty after taking the wrong route when delivering in Swansea this morning.
“We are investigating how this happened.”