"Let's forget about #Malala & peers, brave community workers, prisoners of conscience, & give the Nobel Peace Prize to, drumroll, the EU," one person from Egypt named @RawahBadrawi said.
Malala is the 14-year-old girl campaigning for education rights who this week was shot in the head by the Taliban in Pakistan, sparking worldwide outrage.
Explaining this year's prize decision, Nobel Committee president Thorbjoern Jagland pointed to the three wars fought between Germany and France in the past, which he said was "unthinkable" today.
"This shows how, through well-aimed efforts and by building up mutual confidence, historical enemies can become close partners," he said, adding the union and its forerunners had advanced democracy and human rights.
But many on Twitter wondered why the prize was given to a union of states currently wracked by a severe financial crisis, which has led to high unemployment and violent protests in some countries.
"Anti-austerity protests in Portugal, Spain, Greece, Italy & France, Nationalism, Fascism, unemployment and poverty. Yeah EU deserves it!" @AnonOpGreece said on Twitter.
Some netizens however leapt to defend the Nobel committee, including one netizen from the Maldives, which has been racked by political turmoil and violent demonstrations over the past year.
"Congrats #EU for the well-deserved #Nobel 4 championing democracy. Hope this emboldens your efforts to restore democracy in the Maldives," @shafeeu said.
"Today's #Nobel Peace Prize has the potential to move minds. Europeans may remember that it's not only the economy, stupid! [No offense Bill]," another named @jonashelseth said, alluding to a well-known phrase from former US president Bill Clinton's campaign.
On a more practical level, many on Twitter wondered who would be picking up the prize money and where the $1.2m would go.
"Does the prize money go to the EU? Perhaps they can use it toward the Spanish bailout," @jbarro said.
"Do I get a share of the Nobel Prize money and do I get it twice since I am bi-european now?" @ntlk joked.