Last night, Woakes bowled two overs in the eight-wicket win over Bangladesh before leaving the field.
"He's obviously been very impressive for us over the last couple of years, and a mainstay, very reliable guy. And it is a worry when he goes off the field and can't come back on and bowl," Morgan said after the match.
"He's going to have a scan tonight and we should have the results either late tonight or early tomorrow morning.
Morgan said his team has the firepower in the pace department even though Bangladesh managed t post a 305-run total on the board.
More From This Section
"I think some of the guys today picked up the load pretty well. You know, when one of your main bowlers can only bowl two overs, it's asking a lot of the rest of the team to be able to stem the flow," he said.
"At one stage, Bangladesh looked like they were getting 330, and to peg it back from there I thought was a credit to them. They adapted to the longer boundary pretty well, and to wicket -- it was a really good wicket to bat on. I thought they did well."
"So that contributed to what we wanted to -- how we wanted to balance the side and how we sort of had foreseen them playing. Their top three batters are lefties, and the possibility of getting Joe or Mo on early was an option."
Joe Roots, who scored his 10th ODI hundred yesterday, had suffered a cramp in his calf while batting and Morgan allayed fears over his fitness.
Morgan was happy with the way his bowlers performed in the final overs to stem the flow of runs.
"Obviously when you have an in-batsman in, it can be very destructive, particularly at that period, when he's obviously 80, or goes on and get a hundred and passed then.
"But I thought our bowlers did really well managing his strike rate and then taking two wickets on the bounce. I thought he did a great job."
"I think in the middle patches, we couldn't get any wickets. Obviously with eight batters, we are in a great position to score 330, 340. But we couldn't. We lost too many wickets in the late order."
"After Tamim got out, then Mushfiqur, the next ball, that was the problem for us. I think we were 20 to 30 runs short, especially on that sort of wicket.