Nick Panay, from the Royal College of Obstetricians and Gynaecologists, told a GPs' conference that it could also improve women's energy and mood.
But he said there were no licensed testosterone products for women, who need much lower doses then men.
Around one in three women is affected by the condition at some stage in their lives.
Mr Panay, consultant gynaecologist at Chelsea and Westminster Hospital NHS Foundation Trust, said there was a need to tell women about the potential benefits of testosterone.
He told the Royal College of GPs' conference in Harrogate: "We're not saying that female androgen replacement is a universal panacea.
"We're not saying it is a female Viagra. Women are, after all, much more complex creatures than men (and do not respond) to the on/off button that Viagra offers.
"But I think that it should be part of the counselling process."
He said he believed testosterone should be made available to all women who could benefit. Loss of libido affects 15% of menopausal women.
The medical term for the condition is hypoactive sexual desire disorder, which can also be caused by medical or mental health problems, hormonal factors and relationship issues.
He said patients who had taken testosterone had reported huge increases in their mood, energy, muscle strength and stamina.
Mr Panay said: "They go from feeling drained to being able to run marathons again."
Since there are no licensed products available for women, he had to prescribe it "off-label" which he found "frustrating".
All licensed testosterone medications are designed for men and have to be measured down for women, he said.
Dr Channa Jayasena, a clinical senior lecturer in endocrinology at Imperial College London, said testosterone can be given to women in much lower doses than men.
He said: "It's mainly given in a patch. Women have both sex hormones - oestrogen but also testosterone - made by their adrenal glands and also the ovaries.
"It is a natural hormone but less is known about its effects."
Last year, GPs wrote more than 370,000 prescriptions for testosterone, which costs the NHS Â£21.3m annually.
Women suffering from a loss of sexual desire should be offered testosterone on the NHS, a doctor has suggested.