West Brom say Jake Livermore confronted a West Ham fan at London Stadium after a comment was made about the death of his infant son.
The midfielder was involved in an angry exchange after he was substituted in the second half of his side’s 2-1 loss.
Livermore and his partner lost their newborn son Jake Junior in May 2014.
West Brom have offered their “total support” to the England international, 28, and have sent their observations to the Football Association.
West Ham are investigating the incident and said they have identified the supporter involved. The man was spoken to by staff on Tuesday and removed from the stadium, the club said.
In a statement, West Brom said: “The club would like to think that all right-minded football supporters could understand this reaction which did not result in any physical exchanges before Jake was led away to our dressing room.
“Jake is an outstanding young individual who has the total support of everyone at the club and he has made it clear he considers this statement to be an end to an unhappy incident.
“Albion were very appreciative of the swift response by the officials of West Ham in dealing with this matter and are more than happy to leave any further action they deem appropriate in their hands.”
West Ham said: “The player has confirmed he does not wish to make this a police matter, however, given the nature of the allegations, the club will continue to investigate before taking the appropriate action.”
Livermore tested positive for cocaine while at Hull City in May 2015, almost a year after his son’s death, and the FA decided not to ban him because of “the unique nature of circumstances” involved.
In August 2016 he told BBC Sport: “It was a young human being who got lost in circumstances and didn’t know how to react.”