Merino suffered the injury during the Premier League match against Manchester United just over a week ago.
The 29-year-old was substituted at half-time and scored in the match, which ended in a 2–3 loss for Arsenal.
However, his foot sustained a heavy blow and now needs surgery.
"Mikel is expected to be out for an extended period, with the aim of returning to full training before the end of the season," the club wrote in a statement.
Merino has scored four goals and provided three assists in the league this season. In the Champions League, the Spaniard, who sometimes plays as a striker, has scored two goals.
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