Howard, an All-Pro selection in 2020 after leading the NFL in interceptions with 10, jogged off the field after the team's warm-up Thursday before resurfacing some 40 minutes later and watching the end of practice from the sideline. The team provided no updates on Howard's condition.
Howard took to Instagram on Tuesday night to request a trade over his displeasure about his contract.
"I don't feel valued, or respected, by the Dolphins," Howard said in his post Tuesday night. "Just like they can take a business-first approach, so can I.
"I'm one of the best cornerbacks in the NFL, and the tape backs up that claim. Yet, I'm the second highest paid cornerback on my own team, and it's not even close. That's why I want to make it clear I'm not happy, and have requested a trade. Until that trade happens I am just here so I don't get fined, and will handle myself like professionals do."
In 2019, Howard signed a five-year, $75 million deal that, at the time, made him the highest-paid cornerback in the NFL. But he is due $12 million in non-guaranteed money this year while coming off a 10-interception season (the most in the NFL since 2007) that earned him an All-Pro nod.
Howard's contract now ranks sixth in per-year average, and he switched agents recently to navigate his push for a stronger deal.
Howard, a second-round draft pick in 2016, skipped the entire offseason program, including the Dolphins' mandatory June minicamp, subjecting himself to fines in excess of $90,000.
ESPN's Jeremy Fowler and The Associated Press contributed to this report.