The fourth-round draft pick and wide receiver from Florida, who arrived in Cleveland with a history of issues while in college, was cited early Sunday morning for marijuana possession and driving with a suspended license.
The NFL is looking into the matter, with league spokesman Brian McCarthy saying it will be reviewed under the NFL-NFLPA substances of abuse policy.
Callaway was pulled over by Strongsville, Ohio, police at 2:59 a.m. Sunday. According to a police report, Callaway failed to yield to oncoming traffic and a "small amount" of marijuana was found under his seat.
He also was driving with a suspended license.
"We're aware of the citation [and] are in the process of gathering more information and will comment further at the appropriate time," the Browns said in a statement.
Browns coach Hue Jackson said the team "will have a very strong conversation" about Callaway once it has "all of the facts."
"I want to know more about it," Jackson told reporters Tuesday. "Obviously, I am disappointed in it, but I need to understand exactly what happened.
The Browns selected Callaway in this year's draft despite his troubled past at Florida. He was suspended last season for involvement in a credit card fraud case. He also tested positive for marijuana at the NFL combine in February.
Callaway was already in Stage 1 of the league's substance abuse program because of his diluted sample. He could be subject to a fine because of this infraction.
"We have kind of laid out what our expectations are. We said what we do and what we do not do," Jackson said. "Like I said, my job is to make sure that I look into these things, understand them all, and then, the person has to deal with the consequences that comes with it.
"We do not take things lightly, but at the same time, until I know everything about it, I do not want to make a strong comment one way or the other."
Jackson said he has talked "quite a bit" with Callaway since the team drafted him.
"This is surprising to me. It is," Jackson said. "... He has been great. We have had no slip-ups, no issues. This is a young player, who obviously made a bad decision or bad choice. I have to find out."
Gordon has been suspended multiple times by the NFL for violations of the league's substance abuse policy.
The team has also considered signing free-agent receiver Dez Bryant, the former Pro Bowler released earlier this year by Dallas.
In April, Browns general manager John Dorsey felt confident the team had done its homework before taking Callaway in the draft.
"I feel very comfortable with where we are as an organization," Dorsey said. "We have done extensive -- I mean extensive -- background work here. We actually have had people go down to Gainesville. We have actually had people go down to certain areas just to find out all about the specifics of the situation.
"We feel very good about where we are, where he is and where those things you were talking about, where those are at. I feel very comfortable with where we are to make a move like this."
Callaway's off-the-field problems at Florida were extensive.
In 2017, he was cited for marijuana possession as a passenger in a car driven by a known felon. Callaway pleaded no contest to possession of drug paraphernalia and was fined.
A year earlier, he was accused of sexual assault, prompting the university to suspend him while the incident was investigated. Callaway eventually was found not responsible during a student-code-of-conduct hearing, but he acknowledged under oath he was high on marijuana at the time of the alleged assault.
"Absolutely. No doubt," Jackson said when asked if he was alarmed due to Callaway's past. "We cannot run from that. Obviously, the red flag is up, because that is something that he has had."
The Associated Press contributed to this report.