The 34-year-old required surgery following his loss via a unanimous points decision at Wembley’s SSE Arena on November 18.
Gutknecht fell ill in his changing room after the fight and was subsequently taken to hospital with the British Boxing Board of Control confirming his is in a "stable condition".
Groves, who retained his WBA International super-middleweight title on the night, has set up a fund to help the boxer and his family.
He took to social media on Wednesday to provide an update and urge the public to donate to the crowdfunding page.
Groves Tweeted: "Out of respect for Eduard and his family’s privacy I haven’t Tweeted anything about his medical situation so far.
"However, he is still in hospital in a coma after having surgery the night of our fight 12 days ago.
"Thank you to my friends and family who have already donated, it’s much appreciated."