SHR said through its official Twitter account that Gibson, 51, will stay home in North Carolina to care for his wife, who is dealing with an unspecified illness. The team indicated that Gibson planned to rejoin the No. 41 team in time for Saturday's Duck Commander 500 (7:30 p.m. ET, FOX, PRN, SiriusXM NASCAR Radio), the seventh NASCAR Sprint Cup race of the season.
Johnny Klausmeier is serving as interim crew chief in Gibson's absence, according to the team.
"It's a good way to gauge how well we're prepared for situations like this," Busch said. "Tony Gibson's a great leader and everybody's ready to step up when he's gone."
Gibson joined SHR in 2009. He has been paired with Busch since the end of the 2014 season, winning two races with the former premier-series champion in that span.