The forward has been on admission since last Wednesday on an undisclosed ailment after complaining of paralysis in his legs.
Club chairman Victor Rumson Baribote confirmed the incident.
"I spoke to his brother and he told me that he was complaining of pains in his leg after training last week and he was taken to hospital," Baribote told KickOffNigeria.com.
"He was later paralysed just before his death."
Baribote said the club were shocked to hear the news and had requested to be involved in all arrangements.
"We are shocked. I have asked the family to keep us informed about the plans they are making, and we will try to be involved as much as possible."
Baribote also said he is yet to cme to terms with the tragic news.
"I spoke to him just last week when I was trying to explain to him how we were working hard to make sure their money is released so we can pay them what they are owed. This is shocking."
Ameh is the second Nigerian footballer to die this month, following Bobsam Elejiko who died earlier this month. Two years ago, Bayelsa United captain Abel Tador was killed in a robbery after the club secured their first ever title in 2009. Ameh was a member of that squad.