Perry, 30, broke his arm while attempting a tackle in the Crusaders' 24-22 victory over the Blues in their Super Rugby opener at Eden Park on Saturday.
He had been on the field for just seven minutes before starter and fellow All Blacks prop Joe Moody was forced to return to replace him.
"He will go see a specialist on Monday to have a look at the options," Robertson said of Perry's arm. "If it's an operation, and how long that would take to recover, if it is.
"(I'm) really gutted for him. He's in incredible shape, probably the best of his career. It's tough for him and the team because we need him. We wish him a quick recovery."
Moody's return to the field actually stabilised the Crusaders' scrum after the Blues had brought their two All Blacks props Karl Tu'inukuafe and Ofa Tuungafasi on as second-half replacements and put pressure on the visitors.
Robertson was impressed with Moody's lengthy game time, especially since he had not played since late October.
Moody suffered an eye injury ahead of the England test last November and was ruled out of the remainder of the end-of-season tour. He also did not play any pre-season games.
"I think he played better the second time around," Robertson said of Moody's performance, which included helping the Crusaders dominate the Blues scrum and earn a penalty try.
"Massive shift for him. He was our players' player-of-the-day, just because the amount of effort he put in.
"Pretty special performance from Joe first game back. Incredible."
Robertson said the Crusaders still had options at loosehead prop with Harry Allan and Donald Brighouse in their wider squad as they prepared for their clash next Saturday against the Hurricanes in Christchurch.
The John Plumtree-coached Hurricanes also have an injury concern heading into the game with utility back James Marshall suffering a dislocated shoulder in their 20-19 win over the Waratahs in Sydney.
Marshall's injury has exposed depth concerns at first five-eighth for the Hurricanes, with Beauden Barrett not expected to be available for the Crusaders match. The All Blacks playmaker got married during the off-season and was only returning to the team from his honeymoon this week.
Despite Fletcher Smith's shaky start in the position against the Waratahs, Plumtree said he was not going to hurry Barrett back.
"Beauden will be back in next week, but we won't be rushing him back," Plumtree said.
"We've obviously got Jackson Garden-Bachop to fall back on and Beauden coming back, eventually, so it's not all doom and gloom."