Saturday's race was run in near-record heat in Baltimore.
"We are going to stay with our plan of what's best for Ritchie," Rich Strike's owner said in a statement days after the horse won the Kentucky Derby.
His horse that won the 2021 Kentucky Derby, failed a second drug test that detected a banned steroid.
Baffert is suspended from all three major race tracks in New York, including Belmont Park, which will host the Belmont Stakes on June 5.
Medina Spirit, the Kentucky Derby winner, finished third after a pivotal week that saw the horse test positive for banned substances.
Kentucky Derby winner Medina Spirit is the bookmakers' favorite and drew post No.3, which last produced a winner in 2014.
Dry weather and mostly sunny skies are expected at Pimlico Race Course in Baltimore on Saturday for the second leg of the Triple Crown.
Medina Spirit won the 147th Kentucky Derby on Saturday. Here are the final results from the first leg of horse racing's Triple Crown.
"Essential Quality" is the 2-1 favorite ahead of the 147th instalment of the Run for the Roses this Saturday.
The 147th Run for the Roses on Saturday will welcome back fans after having been held behind closed doors last year.
A year after the Derby was held behind closed doors, up to 48,000 fans will attend the Run for the Roses at Churchill Downs on Saturday.
The Kentucky Derby has been postponed until September, but new horse races are coming to Churchill Downs sooner than you might think.
A failed drug test should have resulted in a disqualification for the Kentucky Derby, making it impossible for him to win the Triple Crown.
Justify will race for the Triple Crown Saturday.
Mastery's ankle injury forced an early retirement.
Wins Belmont Stakes with Victor Espinoza aboard, becoming 12th horse to capture the Triple Crown.
The last Triple Crown winner was Affirmed in 1978.
Last year's Stakes were plagued by huge crowds, over 100,000 total.