Hincapie came on for the final 10 minutes of Saturday’s 2-1 win over Leeds in the Premier League.
Hincapie has been assessed since then and while no confirmation of the severity of the injury has yet been provided, he was absent on Monday.
There had been suggestions that midfielder Zubimendi also picked up an issue in the warm-down after the Leeds game.
And he was similarly not involved on Monday as Arsenal trained in front of the media at London Colney ahead of their Champions League match at home to Lille on Tuesday night.
Manager Mikel Arteta will hold his pre-match press conference later on Monday, when he will provide an update on both Hincapie and Zubimendi.
Doubts: Arsenal may be without both Piero Hincapie and Martin Zubimendi against Lille
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If Hincapie is ruled out of facing Lille, Arteta will face a selection dilemma in defence.
Riccardo Calafiori has been one of Arsenal’s best players this season and has started every Premier League match so far.
However, Calafiori has not played a single minute in any other competition, with Arteta prioritising his availability for league action.
Hincapie’s absence could force Arteta’s hand on Tuesday night, though the Arsenal boss would have the option of shifting Myles Lewis-Skelly from midfield to left-back instead.
There are not believed to be any other fresh injury concerns for Arsenal ahead of Lille’s visit to north London.
Ezri Konsa and Kai Havertz both returned from issues picked up over the international break to start against Leeds and seemingly came through that without any setbacks.
Christos Tzolis remains sidelined with the hamstring injury he suffered while on Nations League duty for Greece, while William Saliba is still out with the back problem he exacerbated at the World Cup in the summer.