Elliot was injured during Ireland's 2-2 international friendly draw against Slovakia on Tuesday and Newcastle, who are 19th, revealed he has damaged his anterior cruciate ligament.
"Rob has returned to Newcastle and has been assessed by the club's doctor," a Newcastle statement read.
"He will now commence a programme of treatment and rehabilitation. Regrettably, the severity of this injury will rule Rob out for a number of months.
"Everyone connected with Newcastle United wishes Rob the very best for his recovery."
Thank you to everyone for their kind messages.will come back stronger! feel so lucky to have so much support behind me. Love to everyone — Robert Elliot (@the_dilsh) March 30, 2016
It marks a further blow to Newcastle's battle to avoid relegation from the Premier League, with first-choice goalkeeper Tim Krul also absent with a serious knee injury.
Karl Darlow is set to play between the sticks when Newcastle visit 17th-placed Norwich City on Saturday in a crucial encounter at the bottom of the table.
Ireland qualified for the European Championship in France by beating Bosnia-Herzegovina in a play-off, and they will face Sweden, Belgium and Italy in the group stages.