"We couldn't be confirming worse news," the La Liga club said on Twitter, BBC Sport reported.
The Spaniard joined the Gunners from the La Liga side in January 2004 and was part of the 'Invincibles' side that went through the 2003-04 season unbeaten, winning the Premier League.
He later spent a season on loan at Real Madrid in 2006-07, winning La Liga.
The La Liga club paid tribute to the "eternal legend", adding he was "one of the most valuable home grown players in the history of the club".
Reyes leaves behind his wife Noelia Lopez, who he married in June 2017, and three children, daughters Noelia and Triana and son Jose Antonio Jr. from a previous relationship.
Henry leads tributes
Arsenal paid tribute to its former player, saying it is "devastated by the shocking news".
Gunners legend Thierry Henry, who played alongside Reyes between 2004-2007, called him a "wonderful player, superb teammate and exceptional human being".
"I wish his family and friends continued strength and courage to get through this difficult time. #takenfartoosoon", he added on Twitter.
Ex-teammate Freddie Ljungberg said, "Numbed by the news about my former teammate, Jose Antonio Reyes. Gone far too soon, my thoughts are with his family and friends."
His current club Extremadura said in a statement on Twitter, "With a broken heart Extremadura UD announce the death of their player Jose Antonio Reyes in a traffic accident."
Reyes' final match was a 1-0 win at Alcorcon on May 18. The Spanish second division side is scheduled to face Cadiz away from home today.
Career full of trophies
In the 1999-2000 season, Reyes made his debut aged just 16 years old – the youngest in Sevilla's history.
After leaving the Gunners in 2007 he won the Europa League twice at Atletico Madrid and three times at Sevilla.
In January, Reyes, who won the 2010 World Cup with Spain, joined Spanish second division struggler Extremadura.
Last year, it was reported that Reyes was set to return to Arsenal as a coach under Unai Emery, who he played for at Sevilla.
Reyes joined Arsenal in a deal worth about £17 million in 2004 and in May 2005, he became the second player to be sent off in an FA Cup final, as Arsenal beat Manchester United in a penalty shootout.
He also played in the 2006 Champions League final as the Gunners lost 2-1 to Barcelona.