The 27-year-old damaged a finger while keeping wicket in the County's win over Glamorgan last weekend.
And although the good news is there is no fracture, the clash at Headingley which starts on Thursday will come too soon.
"It's not a break, but he has done a bit of damage," confirmed head coach David Ripley
"He is really struggling to bend the finger at the moment, but at this stage we are still hopeful he will be available for the Sussex game (starting on May 6), but we will have to see."
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Rossington's injury means Ricardo Vasconcelos will keep wicket as well as open the batting.
Elsewhere on the injury front, left-arm spinner Simon Kerrigan has been given the all clear to play after undergoing a fitness test at the County Ground on Tuesday morning.
Kerrigan suffered a side strain in the recent loss to Lancashire, but he is fit and will be been included in the squad to travel to Leeds, as will pace bowler Brandon Glover.
Glover has yet to feature in the first team this season.
Batsman Alex Wakely, who hasn't played since the opening game of the season against Kent, will again be absent for personal reasons.
Tom Taylor could return having been rested for the win over Glamorgan, with Ripley set to once again shuffle the pack when it comes to his pace bowling attack.