The 23-year-old sustained a knee problem during the Tigers' victory at Millwall on Saturday and has been sent home after reporting for international duty.
Leeds midfielder Paul Green has been drafted into the squad as a replacement for Meyler and will link up with the squad in Portmarnock in time to take part in
training at Gannon Park on Wednesday morning.
Ciaran Clark and Shane Long did not train with the squad in Malahide on Monday but assistant coach Marco Tardelli revealed the duo were both rested.
Clark has a minor knee injury while Long played the full 90 minutes of West Brom's defeat against Tottenham on Sunday.
And one player who declined the offer to join up with the squad was Everton's Darron Gibson.
The 25-year-old Everton midfielder has not played for his country since opting to take a self-imposed exile following the Euro 2012 finals when Gibson remained on the Irish bench.
Tardelli revealed that manager Giovanni Trapattoni contacted Gibson on Monday following Meyler's withdrawal from the squad but said he was not interested because of his own fitness concerns rather than a desire not to return.
Tardelli said: "Darron told us that he has played just one match and would prefer to stay at home.
"I think Darron wanted to come here with us. He is not available for this match. He was in Malaga because there is training camp with Everton."
Tardelli stressed that Gibson would be considered for selection for the forthcoming World Cup qualifiers against Sweden and Austria in March.
Gibson was named in the squad for the Republic's first qualifier in Kazakhstan in September of last year but withdrew after telling Trapattoni he was disappointed by what happened in Poland during the summer.