Rhine, a popular figure, was the club's television commentator and had also worked in community development after playing 212 games in MLS for the Texas-based team.
The club said Rhine had passed away suddenly on Monday evening while a report on ESPN's Dallas website said he had died of "an apparent heart attack."
"It is an extremely sad day in the history of FC Dallas," club president and CEO Doug Quinn said in a statement.
"Bobby was the voice and face of our club and always a very popular figure with our fans. Everyone connected with FC Dallas has been affected by this tragic news and we wish to send our heartfelt condolences to Bobby's family."
A versatile player, Rhine made 136 starts and scored 23 goals with 34 assists.
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