An additional daily portion of refined white pasta or rice was linked with women reaching the menopause around one-and-a-half years earlier, according to a study by the University of Leeds.
However, an extra daily serving of oily fish such as salmon, mackerel and sardines was associated with a delay of more than three years.
The research, published in the Journal of Epidemiology and Community Health, drew on data from around 14,000 women in the UK, and a follow-up survey four years later.
More than 900 women between the ages of 40 and 65 had experienced a natural start to the menopause by that time.
The average age of menopause was 51, but the researchers found certain foods were associated with its timing.
As well as oily fish, a diet high in fresh legumes such as peas and beans was linked with women reaching the menopause around a year later.
A higher intake of vitamin B6 and zinc also appeared to delay the onset.
The researchers noted that women who go through the menopause early are at an increased risk of osteoporosis and heart disease, while those who do so later are more likely to develop breast, womb, ovarian cancers.
Study co-author Janet Cade, professor of nutritional epidemiology, said: “The age at which menopause begins can have serious health implications for some women.
“A clear understanding of how diet affects the start of natural menopause will be very beneficial to those who may already be at risk or have a family history of certain complications related to menopause.”
The researchers suggest the maturation and release of eggs can be affected by reactive oxygen species and so antioxidants, found in legumes, may help preserve menstruation for longer.
Omega 3 fatty acids, abundant in oily fish, are thought to stimulate antioxidant capacity in the body.
Meanwhile, refined carbohydrates can increase the risk of insulin resistance, interfering with the activity of sex hormones and boosting oestrogen levels.