The crash happened at Nkawkaw, some 150 kilometres (95 miles) by road from Accra at about 10:00 pm (2200 GMT) on Wednesday, said Eastern region police spokesman Thomas Obeng Asare.
The Premier League side was heading back to the central city of Kumasi after a 1-0 defeat to Inter Allies in the capital.
"The driver of the bus ran into the truck that was loaded with fertiliser and almost 37 passengers sustained various degrees of injuries," said Asare.
The Head of the Medical Team, Dr. Michael Leat has been teaming up with medics at KATH to attend to the injured and all other victims.— Asante Kotoko SC (@AsanteKotoko_SC) 13 July 2017
"They were rushed to the Holy Family hospital at Nkawkaw where some were treated and they have since been referred to the Komfo Anokye Teaching Hospital (in Kumasi)," he said.
"Unfortunately, the team's equipment officer died on the spot and the body has been deposited at the hospital."
An investigation has been launched into the accident.
"Porcupines" to release more details
The club, nicknamed the Porcupines, confirmed the crash in a statement on its website and said more details would be released later.
The Ghana Football Association (GFA) said it was "devastated by the sad development" and had sent a delegation to meet the club and offer its support.
"The GFA has establishsed contact with the club and our thoughts and prayers are with Kumasi Asante Kotoko, particularly the injured officials and players," it added.
Asante Kotoko are due to play Accra Hearts of Oak in Kumasi on Sunday but there was no immediate word on whether the match would still go ahead.