Hayes was stretchered off after a clash of heads with Wasps defender Daryll Meggatt. as Aberdeen beat the Scottish Championship side on penalties following a goalless 120 minutes at Pittodrie.
The Irishman, who Aberdeen say was kept in hospital as a precaution before being released in the morning, will be a major doubt for Saturday's Scottish Premiership clash with St Johnstone.
And both Josh Magennis and Willo Flood are also in danger of missing the visit of the Perth side.
Magennis has a shoulder injury while Flood will go for a scan on a hamstring injury on Thursday, but the club say he looks set to be on the sidelines for a "couple of weeks".
McInnes was already without midfielder Barry Robson, who underwent exploratory knee surgery earlier this month.