Gunners boss Mikel Arteta revealed Merino suffered the injury setback in his first training session with the club when teammate Gabriel Magalhaes accidentally fell on him.
Merino only joined Arsenal from Real Sociedad earlier this week and was in contention to make his first appearance in Saturday's Premier League clash with Brighton.
Instead, Merino, who came off the bench to help Spain win the Euro 2024 final against England, will spend his first few weeks in north London on the treatment table.
"It's very unfortunate. Yesterday (Thursday) he had a collision and he's got a shoulder injury and it looks like he'll be out for a few weeks," Arteta told reporters on Friday.
"It was in his first session with us. It's really bad luck, we were all excited, everything was looking good. He landed on the floor, Gabriel fell on top of him and it looks like he has a small fracture.
"He was in so much pain, we have to see. He'll do more tests which will have more conclusive answers."
Meanwhile, Arteta said Arsenal are set to sign a goalkeeper before the transfer window closes on Friday evening.
England keeper Aaron Ramsdale left Arsenal to join Southampton on Friday after losing his place to David Raya last season.
The Gunners are reported to have agreed a loan deal for Bournemouth's Neto to serve as Raya's back-up.
'Build the numbers'
"When he joined he brought a lot of joy, charisma and energy and he was good at that time," Arteta said of Ramsdale.
"Things developed and there was a situation where things were difficult for him and he insisted that he is happy when he plays so we had to fulfil that desire he had.
"We lost Aaron and Karl (Hein), we need to replace them both."
Arteta has also been linked with Raheem Sterling, but refused to comment on a potential move for the out-of-favour Chelsea forward.
"You know that I can't talk about any other player," he said.
"In terms of the numbers and the quality, can we improve the squad? For sure there are margins there.
"We know about the depth of the squad and it's something that we cannot change dramatically in one or two seasons.
"We are constantly trying to build the numbers, which is something critical, and on top of that bring more quality."
Arsenal have won their opening two games of the season as they look to finally end Manchester City's reign as champions after finishing second for the last two years.
But Brighton could pose a tricky test for Arteta's men, with the Seagulls' new manager Fabian Hurzeler masterminding a pair of victories including last weekend's surprise success against Manchester United.
"We try to prepare like every manager and team. We have to do the same against a team tomorrow who are doing really well against a coach who brings a new regime in what will be a tough match," Arteta said.
