An official at Cryos International said this causes a problem for childless Indian expatriates, reported Daily Telegraph.
The sperm bank has also begun turning down red-headed donors as there is little demand for their sperm.
Cryos's director Ole Schou said that due to an increase in donations in recent years, the facility has become much more picky about its donors.
"There are too many redheads in relation to demand," he told Danish newspaper Ekstrabladet.
Schou said the demand for sperm from redheaded donors was mainly in Ireland where it sold "like hot cakes".
Sperm from donors with brown hair and brown eyes was in demand due to the bank's large customer base in Spain, Italy and Greece.
Denmark-based Cryos sends its semen to over 65 countries worldwide.
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