The authors base their findings on 57, 664 women, who were quizzed about their use of HRT and development of asthma symptoms every two years between 1990 and 2002.
All the women were taking part in the French E3N study, which includes almost 100, 000 women born between 1925 and 1950, and is the French component of the European Prospective Investigation into Cancer and Nutrition (EPIC).
None of these women had asthma when menopausal symptoms began.
The monitoring period equated to 495,448 person years in all, of which over a third was accounted for by women who had not used HRT (35.7%).
Previous users made up 4.5% while information on how long HRT was used was not known for a further 4%. Of the remainder, just under 56% were recent users of HRT.
Between 1990 and 2002, 569 women were newly diagnosed with asthma, corresponding to a rate of 1.15 cases per 1000 women a year.
Compared with women who had never used any form of HRT, those who did use it were 21% more likely to develop asthma, after adjusting for factors likely to influence the results.
Almost one in 10 women with a natural menopause (9.4%), and more than one in four (28%) of those with a surgically induced menopause, used HRT containing oestrogen alone.
The risk of asthma was significant only among those using oestrogen alone. Among these women the overall risk of asthma was 54% higher than among those who had never used any form of HRT.
Oestrogen only users who had never smoked and those who had had some form of allergy before their asthma diagnosis were at greatest risk of developing asthma— 80% and 86% higher, respectively.
A small increased risk for asthma was also seen in women using combined oestrogen and progesterone HRT who were either non smokers or who had had some form of allergic reaction in the past.
Previous research has suggested that female hormones may have a role in the development and severity of asthma, say the authors.
The disease is more common in young women after they have started having periods, while hospital admissions for asthma are more common among women than men.
The severity of asthma also varies throughout the menstrual cycle and during pregnancy, and the incidence of the disease tends to fall after the menopause, except among those who put on a lot of weight, the authors point out.
They conclude that while their findings point to an increased risk of asthma, this must be judged in "the light of all the other health effects of HRT use, including its beneficial effect on the quality of life of menopausal women."