The duo were travelling on a minibus when it crashed following the side’s 1-1 draw with Kayserispor.
Sural was rushed to hospital but later died, while six others reportedly suffered minor injuries.
Among them were former England and Liverpool star Steven Caulker and ex-Newcastle star Papiss Cisse.
A representative for Caulker, who won one cap for the Three Lions, told Mirror Sport he is “safe, but badly shaken up”.
The group had hired the Mercedes to travel back from the game before it went off the road near the city of Alanya.
The rest of the squad had made their way home with the team bus or on their own.
Club chairman, Hasan Cavusoglu, said he had been told by police two drivers were asleep before the crash.
He said: “According to information I received from our police chief, despite there being two drivers on the vehicle, they were both asleep.
“The crash happened as a result of them both being asleep.”
They have been detailed by police as they probe the crash, according to reports.
Sural, who suffered a head injury, had come on as a substitute in the game.
The dad-of-two, who died aged 28, won 20 caps for his country and scored once.
Czech legend Petr Cech wrote on Instagram: “Very sad news from this morning. RIP Josef Sural.”
And the Czech FA tweeted: “The Football Association of the Czech Republic has accepted with great grief the news that the representative striker Josef Sural died tragically in Turkey.
“We’ll never forget you, Pepo!”