Emergency workers were called to Richard Onslow Court, in Hearne Way, Monkmoor, at 6.50am on Friday.
A crew based at Shrewsbury Fire Station was able to switch off the water supply following the incident.
Earlier on Friday crews in Telford were called to douse a small kitchen fire at a property, in Villa Court, Madeley,
Three crews from Telford Central and Tweedale fire stations went to the address at about 2am.
They wore specialist breathing gear and also used a pressure fan to ventilate the smoke.