One of the gliders crashed to the ground while the other was able to carry out an emergency landing and both pilots escaped serious injury.
The incident took place at Portmoak Airfield, near Scotlandwell, where another glider pilot died in an accident in September 2012.
A Police Scotland spokesman said: "We are dealing with an incident which occurred about 3:05pm near to Portmoak Airfield, Scotlandwell, where two gliders collided with each other in mid-air.
"One glider impacted with the ground and the other made an emergency landing. The pilots of both gliders were alone in the aircraft.
"One pilot was uninjured and the other pilot has been conveyed to Victoria Hospital in Kirkcaldy for treatment but it is believed that he has only minor injuries."
It is understood the aircraft were close to the ground when their wings clipped and one spiralled out of control and nosedived to the airfield.
Portmoak hosts the Scottish Gliding Centre. It is the country's largest club and offers training courses and aerobatics lessons.
In September 2013, a 75-year-old man from Edinburgh was taken to hospital after crashing his glider at the same airfield. He crashed on landing and his aircraft was extensively damaged.