It said the fire broke out while the rig was being readied to be moved, and that it was extinguished by GDI firefighters and Qatar Petroleum emergency services.
The company did not say when or where the incident happened, nor where the rig was being moved to.
"Injured personnel consisting of six GDI employees were immediately transported to nearby hospitals and most of them discharged after having received treatment," the statement read.
"The rig named GDI-3 was moved to another location where it was repaired and put into service again."
On its website, Gulf Drilling International says it was the first onshore and offshore oil and gas drilling company to be established in Qatar.