Robinson, who has enjoyed 14 appearances for the Gills since arriving in January on a deal until the end of the season, will now undergo a knee operation and faces a lengthy spell on the sidelines.
The news comes as a big blow to Gills boss Martin Allen, who had eyed Robinson as a potential summer transfer target for next season's campaign in League One.
Allen said: "Anton's a fantastic player. He's a great lad on and off the field. He conducts himself superbly well.
"When I found out what it was, he's obviously got to have an operation to repair that. The recovery time is generally between six to nine months. He's a very, very fit lad. He's got a great work ethic so I wouldn't be surprised to see him back in six.
"He's got another year to go on his contract at Huddersfield which, for him, is a big relief of course."