The Danish side said the 28-year-old lost consciousness at his home on February 20 and was taken to a local hospital in Aarhus, Denmark, where he continues to receive treatment.
Olsson, who has played 47 times for his country and once represented English Premier League club Arsenal, has been surrounded by immediate family and club staff since being admitted to hospital, the team added.
“Everyone at FC Midtjylland is of course deeply affected by Kristoffer’s sudden illness and our thoughts and full support go out to Kristoffer and his family,” the club said in the statement.
The club said it released the statement after rumors started spreading online about Olsson’s continued absence from the team. FC Midtjylland also asked for privacy to allow the midfielder and his family to focus on recovery.
FC Midtjylland said on Wednesday that training had been closed to media and fans as the club had been so affected by what had happened to Olsson.
Former club Arsenal, where Olsson spent three seasons after joining as a teenager, wished the midfielder a “full and speedy recovery” in a post on X, formerly known as Twitter.
After leaving Arsenal in 2014, Olsson joined FC Midtjylland on loan before completing a permanent move to the Danish side.
He then left to play for the likes of Belgian side Anderlecht and Russian club Krasnodar before returning to Midtjylland in 2022.
In a post on social media, world soccer governing body FIFA also offered its support to the Swedish star.
“Sending our wishes to Kristoffer and his family at this difficult time,” it wrote on X.
The Swedish Football Association’s head of football Kim Källström also sent his thoughts to the player.
“You feel genuinely sad at heart by the news of how a young person can be affected in this way,” Källström said in a statement.
“All our thoughts go out to Kristoffer and his family. It feels so incredibly sad.”
