Mumsnet, which has more than one million members in the UK, is the first company in Britain to announce data loss, and the announcement comes just two days after a post on the site's forum informed users that all passwords would be reset as a security measure.
Last week, blogging site Tumblr urged all users to change their passwords immediately to prevent personal and sensitive data being stolen.
The Institution of Engineering and Technology described the Heartbleed bug as a "serious software defect", while independent online security expert Bruce Schneier said "On a scale of one to 10, this is an 11", when news of the defect first appeared last week.
Mumsnet has vowed to keep users notified of any new information they receive.
Ms Roberts said: "The security of our users' data is of paramount importance to us. We collect very little of it, and we never pass or sell it on without people's explicit consents.
"Heartbleed has shown that nobody can offer a 100% guarantee of online security, but we'll continue to do our best to protect our users as much as we can, and be transparent about any breaches we find."
