Roy suffered a hamstring tear in Friday's win over West Indies and Morgan confirmed James Vince, who had a lengthy net session at Old Trafford on Monday, will replace the opener on Tuesday.
"I certainly believe Jason will play again in this tournament," Morgan told reporters.
"At the moment he's going to be assessed continuously over the course of the next week. He's out of the next two games. So we'll see how he pulls up after that."
Roy made a superb 153 against Bangladesh in Cardiff but his replacement as opener Joe Root impressed with an unbeaten century which sealed an eight-wicket win for the hosts.
The 26-year-old Roy will miss the matches against Afghanistan and Sri Lanka but Morgan is confident he will be back before the June 30 game against India.
"As we know with injuries, people respond differently to treatment and medication, so it's a matter of giving him enough time to allow him to get himself back into the tournament," Morgan said.
Morgan had better news about his own health after suffering the back spasm in the match against West Indies after which he delivered his news conference standing up.
"Yeah, drastically improved. I've had extensive treatment and medication the last two days, which have helped me no end," said the 32-year-old.
"I've had a small hit in the nets, and hopefully be fit to play in the morning. It will all depend on how I pull up but aiming to play tomorrow."
England are fourth in the table with six points from four matches and will be overwhelming favourites against bottom- placed Afghanistan who have lost all four games.
Morgan refused to be complacent, though, against a spin-heavy Afghanistan.
"It's probably their strongest component as a team. It's a challenge that we're going to have to overcome," Morgan said.
"Pretty much every time we play against an Asian team, that's the case.
"You look over at where they are practising. They are practising against quicks, and look over at our nets and we're practising against spin. That's just a challenge that both sides come up against."
(Additional reporting by Shrivathsa Sridhar in Bengaluru,; Editing by Keith Weir and Ed Osmond)
