The Royal Navy said the exercise on a surface ship triggered a fire suppression system.
Emergency services were called to the naval base just after 05:30.
They were taken to the Royal Alexandria Hospital as a precaution. Their families have been informed, and an investigation has been launched.
A Royal Navy spokesman said: "We can confirm that there has been an incident on a surface ship alongside HM Naval Base Clyde this morning.
"A routine fire exercise triggered the fire suppression system, which resulted in a number of personnel inhaling a gas.
"Six personnel were taken to hospital as a precaution; all others were declared fit at the naval base's sick bay."
The Faslane base on the Clyde is home to the UK's fleet of Trident nuclear submarines.
Six Royal Navy personnel have been taken to hospital after inhaling gas during a routine fire exercise at Faslane.