Ofcom reported that just over half of parents it surveyed said they avoided what it termed "sharenting" altogether.
A desire to protect the privacy of under-18s was the most commonly given reason, it said.
But about one in five parents said they posted such images at least once a month, the regulator added.
The figures are contained in the organisation's annual Communications Market Report.
It is based on an online survey of 1,000 adults carried out in April by YouGov.