The West Ham United defender injured his hamstring in their 1-0 Premier League win over Tottenham on Wednesday.
"The first information is that we should be happy if he only misses three games," said Hammers manager Slaven Bilic.
Wales play Northern Ireland at the Cardiff City Stadium on 24 March, and Ukraine in Kiev four days later.
Chris Coleman's Wales team are already likely to be without Real Madrid forward Gareth Bale, who is poised to return to action this weekend after a six-week lay-off with a calf injury.
Bale has not played since injuring his calf in Real Madrid's 5-1 win against Sporting Gijon on 17 January.
Wolves midfielder Dave Edwards says it will be difficult for him to secure a place in Wales' Euro 2016 squad following his foot injury.
The March warm-up games are seen as key fixtures as Wales prepare for the Euro 2016 finals in France.
Collins will miss West Ham's Premier League games against Everton and Chelsea, and the FA Cup quarter-final against Manchester United at Old Trafford this month.
James Collins could miss Wales' friendly internationals with Northern Ireland and Ukraine later in March.