Stroll was ruled out of this week's three-day test after a cycling incident left him with what team boss Mike Krack has now revealed is a wrist injury.
The team still doesn't know if Stroll will definitely be fit enough to take part in the Bahrain Grand Prix next weekend.
Reigning Formula 2 champion Felipe Drugovich took over the car for Thursday morning's session, although his running was compromised by an electrical issue before he handed the car to Alonso for the afternoon - the Spaniard posting the day's second-fastest time.
The team announced on Thursday evening that only Alonso will drive on Friday, although it hasn't yet confirmed its schedule for Saturday.
It's understood that even if Drugovich is listed alongside Alonso for Saturday, it won't necessarily mean that there are still doubts over Stroll's participation in the race weekend, as the team believes that it would still be useful for its reserve driver to complete some more mileage this week.
Aston Martin's other reserve, Stoffel Vandoorne, is currently committed to the Cape Town Formula E event and could not attend the test, but he is scheduled to be in Bahrain for the race weekend.
"He was training, trying to improve or to work on his fitness last week," said Krack when asked about Stroll's situation.
"So he was cycling and he had a small incident and hurt himself. And for precautionary reasons, we decided it's better to wait a little bit, and be ready next week."
However, Krack would not go into details regarding Stroll's condition, adding: "This is his personal thing. So he is injured on the hand, on the wrist. But I don't want to go into detail, because this is also privacy."
Krack said that Drugovich's appearance in the test was in case he is needed for the race weekend.
"He did the morning session today," he noted. "So this is also something that I think you have to do as a team, just to cover all eventualities."
Drugovich completed 40 laps after stopping on track in the opening minutes.
"We had a few electrical issues," said the F2 champion. "Actually just one, but it took quite a bit of time just to get it fixed. But it was pretty straightforward, an easy thing.
"After that we got going, lots of tests for the team, exciting for me. I'm here, obviously, to wish a speedy recovery to Lance. But, while I'm here, I'm having fun and trying to help the team."
Asked about the prospects of him racing next weekend, he said: "We don't know yet. They're evaluating it day-by-day. So I don't even know what's going to happen, it depends on him as well."
Any suggestion that former Aston Martin racer Sebastian Vettel could make a surprise one-off comeback – in much the same way as the recently retired Jenson Button did at the 2017 Monaco GP – is believed to be wide of the mark.
