Jimenez lasted just five minutes in Wolves’ 2-1 victory at the Emirates Stadium before suffering a nasty clash of heads with David Luiz.
The 29-year-old Mexican required lengthy treatment on the pitch before being stretched off and is set to be sidelined for some time in what will be a huge blow to Nuno Esperito Santo’s men.
Wolves have refused to put a timeframe on when the former Benfica striker will return to action but have confirmed that his time in hospital will be cut short next week.
A statement attributed to Wolves doctor Matt Perry on the club's website read: "Following Raul's injury on Sunday, and the subsequent surgery, he has been recovering well in hospital.
"We are delighted with the reports from his specialist; he has made excellent progress. He should be ready to leave hospital by early next week.
"Once home, he will be reunited with his partner and young daughter who, because of COVID restrictions, he hasn't seen since Sunday night.
"As his doctor I am not going to disclose any more details of his injury, his surgery or provide daily accounts of his recovery.
"Any injury of this nature is complex and timescales are uncertain but it's safe to say that Raul’s most immediate needs are simple: space, rest and peace.
"Raul and his family are very thankful for the privacy they have been given, and for the overwhelming support they have felt from the football family and beyond.
"Raul is extremely grateful for all the messages of goodwill he continues to receive, which will certainly help him during his recovery."
Jimenez has been Wolves’ top scorer for the last two seasons and has scored four goals in 10 league games this season.
