She is also putting pressure on Latvian authorities to investigate the lack of safeguards on social media site ask.fm.
This comes in the wake of the recent tragic deaths of two teenagers.
Erin Gallagher, the 13-year-old Co Donegal teenager who took her life last weekend, and 15-year-old Ciara Pugsley from Co Leitrim, who died last month, were both victims of anonymous bullying on ask.fm.
The minister spoke with Simon Millner, policy director for Facebook in Ireland and the UK, about online safeguards for children in light of concerns over cyber-bullying and other inappropriate online behaviour.
She said she was satisfied there were "child-focused and user-friendly safeguards and supports" that Facebook had put in place to protect children.
But she expressed "concern that certain other websites popular among teenagers do not include the same safeguards".
The ask.fm website, which is owned by Latvian-based businessman Mark Terebin, is open to anyone aged 13 or over, and allows users to ask and reply to questions from other users, anonymously. Users can also sign up through their Facebook or Twitter accounts.
Addressing the Digital Youth symposium in Dublin yesterday, Ms Fitzgerald said new technologies had opened a world of opportunity for young people, opportunities which should be accentuated. "But it also brings risks which must be mitigated," she said.
"In seeking to respond to cyber-bullying, we should seek to start by addressing bullying in the round. This requires a whole school-and-community approach to address the underlying factors."
However, the Ombudsman for Children Emily Logan warned that blocking access to the ask.fm website would not end cyber-bullying.
"I don't think blocking one website is going to stop the issue. If anything it would possibly generate even more websites if it creates the amount of attention that it's getting.
"If ask.fm is blocked in Ireland then another website will develop and that's part of the problem.
"This is a complex issue that requires a broader response. It's everything from teaching parents to having reasonable oversight of their children's online activity to educating children."
Ms Logan made her comments at the launch of a report by her office on bullying in schools.
Some 300 children aged from 10 to 17 took part in the report, entitled Dealing with Bullying in Schools: A Consultation with Children and Young People.
Cyber and homophobic bullying were two of the most prevalent forms raised by participants.
It is estimated that more than 10,000 Irish schoolchildren find it difficult to go to school every day as a result of being bullied. And at least 24pc of primary school children and 14pc of post primary school pupils have experienced bullying.
More than 40pc of parental complaints to Ms Logan's office relate to education, and bullying is among the five issues most frequently raised.
The ombudsman also believes there should be an anti- bullying policy in every school
"Sometimes, unfortunately, it takes the kind of trauma that we have seen over the last few weeks for us to react in terms of a public reaction to something as serious as this," Ms Logan said.
Ask.fm website founder Mark Terebin has insisted that it is "just a tool which helps people to communicate with each other, same as any other social network, same as phone, same as piece of paper and pen".