The fault triggered a major alert in the city centre amid fears the 50m crane could topple in high winds.
A major emergency operation was launched involving police, the fire service, ambulance crews and Network Rail while the Park Street area of the city centre had to be cordoned off.
Galliford was forced to evacuate the hotel building site as a precaution and dismantled the tower crane over the weekend.
The firm picked up the fault in the concrete foundations of the crane during a routine check.
A West Midlands Police spokesman said: “Specialists conducting a routine check of the site identified a potential problem with the concrete foundations which fix the crane to the floor.
“As a precautionary measure, they took the decision to alert police and evacuate the site.”
Galliford Try apologised for the disruption. It said it took health and safety seriously and removed the crane as a precaution.