The burst, on the evening of Wednesday 29 August, meant residents were initially evacuated to Ludgate House as a "rest centre".
Chief Executive Elaine McPherson said, "Operational staff from social work, facilities management and roads were swiftly on the scene to manage the incident in accordance with our emergency planning procedures.
"The main priority was to get the 38 Menstrie House residents new accommodation and that was done successfully."
The council's Older People Care Service found alternative accommodation in other care homes within Clackmannanshire, and all staff who normally care for residents will remain with them to ensure the minimum of disruption.
Councillor Les Sharp, convenor of the Housing, Health and Care Committee, who helped with the evacuation of Menstrie House added, "I would like to express my thanks and appreciation to staff from a range of services for the exemplary management of the situation."
Abercrombie Place, Dumyat Road and Burnside Road were also hit by flooding.
The council are in the process of assessing the full extent of the damage to Menstrie House, but it is hoped work can be done quickly to one part of the building so some residents can return this week.
The area to the back of the building, which was worst effected by the flooding, is expected to take two weeks to repair.
The A91 was also closed by police on Wednesday evening because of flooding, as was the Dumyat Centre in Menstrie, both of which the following day.