Both the Old Shoreham Road and Wilson Avenue centres will be open for longer hours from Monday.
If residents are unable to take rubbish to either of the facilities then they are recommended to secure it in bins or containers.
Both the Old Shoreham Road and Wilson Avenue centres can stay open as they are run by external waste contractor Veolia.
Penny Thompson, the council’s chief executive, said: “I am very sorry that our service is being affected during these talks. We will keep you up to date with developments, on our website and through our contact centre.
“We’re doing everything we can to find a resolution.”
Wilson Avenue, Brighton
Until Monday June 17: Open 8am to 4.30pm Monday to Friday and 9am to 5pm on weekends.
From Monday June 17 until further notice: 8am to 8pm Monday to Friday and 9am to 5pm on weekends.
Leighton Road, Hove
Until Monday June 17: 8am to 4.30pm Monday to Friday, 8.30am to 1.30pm Saturday and 10.30am to 1.30pm Sunday.
From Monday June 17 until further notice: 8am to 6pm Monday to Friday, 8am to 5pm Saturday and 10am to 4pm Sunday.