Prior to the tournament, Ghana head coach Carlos Queiroz, said he had no qualms over selecting Partey, who was at Atletico Madrid before moving to London in 2020 to join the Gunners.
"If the player is here with me, my answer is clear," said Queiroz.
"I don't have any comments about my own decisions. He is here so what are we talking about?
"This is not for me or you to make a judgement about.
"Let the events run their normal course; let the river flow and one day when the river meets the ocean we are going to find the truth."
Ghana are set to face England in their second Group L match at the Boston Stadium, Foxborough, on 23 June (21:00 BST) before taking on Croatia on 27 June in Philadelphia (22:00 BST) - both games in which Partey could still feature.
Ghana could potentially return to Canada in the last 32 if they finish as runners-up in Group L. In that scenario they would advance to play the runners-up in Group K in Toronto on Thursday, 2 July.
If they were to progress in third place from their group and win their last-32 match, their last-16 fixture would take place in Vancouver on Tuesday, 7 July.
Partey's situtation is not the first to involve the authorities of the host nations - the United States, Mexico and Canada - as the tournament gets under way.
Iraq striker Aymen Hussein was questioned for several hours at a Chicago airport before being allowed into the country.
Iran have been forced to switch their base location to Mexico, their fans have had their tickets revoked, while members of their delegation were refused visas.
Meanwhile, Somali referee Omar Artan was not allowed into the US because of his "association with suspected members of terror organisations", according to a source from President Donald Trump's administration.
Artan, who held a diplomatic passport and a single entry US visa, told the New York Times this week that he was questioned by border officials over his links to Somali militant group Al Shabab and had told them he knew nothing about the group.
"I had the right papers and everything. I had the right visa," said Artan.
"I'm just simply a referee who's trying to live his dream, the biggest dream of my life, to come to the World Cup."
Artan was voted the 2025 Confederation of African Football men's referee of the year and has been on Fifa's international list since 2018. He was set to be the first Somali to referee at the World Cup finals.
