A bloc of left-wing parliamentarians, of which Sinn Féin is a member, proposed the measure in Strasbourg.
The amendment was defeated by 374 votes to 66.
Sinn Féin said the outcome was disappointing, but it will continue to campaign for special status.
Sinn Féin MEP Matt Carthy, who represents the Republic of Ireland's Midlands-North-West constituency said: "We have already ensured that the European Parliament is in agreement that the Good Friday Agreement should be protected in all its parts.
"Moreover, the European Council's negotiation guidelines support the need to protect the Good Friday Agreement and recognise the unique circumstances on the island of Ireland and the need for flexible and imaginative solutions.
"We are engaging with hundreds of political representatives and officials  from across Europe in order to gather further support for special status for the north within the EU and will continue to do so," he added.
The DUP MEP, Diane Dodds, welcomed the vote: "Since last June, Sinn Féin and others have made a special designated status their big ticket priority for Brexit.
"It is clear that support for this scenario has gained little traction.
"The negotiating guidelines published by the European Parliament and Council earlier this year make no reference to a special designated status and both governments in London and Dublin have failed to back the proposal.
"Ultimately this week's vote by MEPs is further demonstration that Sinn Féin's Brexit charm offensive has failed miserably.
"Moving forward the DUP will continue to work tirelessly, engaging closely with stakeholders across sectors affected, and using our influence both at Westminster and in Brussels, to ensure that our Province gets the best possible deal from Brexit," she added.
After the debate, the Ulster Unionist MEP Jim Nicholson criticised Sinn Féin for using the term "the north of Ireland" to refer to Northern Ireland.
He said: "They say they want "special status", but they cannot even say the name of the region they want this special status for.
"It is clear for all to see that Sinn Fein's concern is not the economic wellbeing of the people of Northern Ireland, rather it is about trying to use the European Parliament as a platform for anti-UK posturing." he added.
A bid to give Northern Ireland designated special status within the European Union (EU) following Brexit has been defeated in the European Parliament.