Motorists should expect heavy delays on one of inner Melbourne's busiest thoroughfares with upgrades to Swan Street Bridge soon to begin.

One in-bound lane on the bridge will be closed until July with drivers being urged to take alternative routes when heading into the CBD.

The government has warned that inbound delays will be up to 20 minutes in the morning peak, 15 in minutes in the afternoon peak and 10 minutes outside those times.

The delays are expected from March 29 as construction kicks off on an additional lane.