Olsson was making progress at Hammel Neurocenter in Denmark as he underwent rehabilitation for a rare inflammatory condition affecting his brain vessels, the club said.
"His physical progress is significant and he is now actively training his walking function and is able to eat independently," Midtjylland said in a statement.
"Although cognitive challenges remain and the prognosis for his full recovery remains uncertain, the specialists at the treatment centre are encouraged by the positive steps Kristoffer has taken.
"It is breathtaking to witness Kristoffer's fight against the disease. His positive attitude, fighting spirit and tireless will to win are an inspiration to us all," the club's manager Claus Steinlein said.
Olsson, who has 47 caps for Sweden, started his senior career at Arsenal and has also played for Swedish side AIK and Belgium's Anderlecht.
