The news of Miklosko's death was first reported by the iSport.cz website, and confirmed by a post on Ostrava's official X account.
Miklosko was the first Czech goalkeeper to make a breakthrough in England. At West Ham, where he played 373 matches, he became a club legend.
He also featured for QPR and was capped several times by Czechoslovakia and then the Czech Republic national teams.
Miklosko enjoyed huge success after signing for West Ham in 1990, establishing himself as first-choice for over seven years at the Boleyn Ground.
The shot-stopper played a key role in getting the London club promoted from the second division in his full debut season and was named the 'Hammer of the Year' in 1991.
"Everyone at West Ham United is deeply saddened by the passing of Ludek Miklosko at the age of 64, following a courageous battle with cancer," the club said in a statement on their website.
"The hugely popular former goalkeeper, known fondly as ‘Ludo’ to the Claret and Blue Army, made 373 appearances for the Club during eight years as No. 1 between 1990 and 1997.
"The incredible impact he had on the Club and the fondness with which he is remembered is heard every matchday, when supporters sing his iconic ‘My name is Luděk Mikloško, I come from near Moscow, I play in goal for West Ham’ chant.
"In June 2023, he joined his fellow Hammers in Prague as West Ham defeated Fiorentina to win the UEFA Conference League, and was moved to tears as the Claret and Blue Army sang his famous song at a fan zone in the Czech capital’s Letna Park.
"Ludek’s last visit to see his beloved Hammers came in December 2024, when he was Guest of Honour at London Stadium for our fixture against Liverpool, having confirmed publicly that he was taking the brave decision to withdraw from further treatment in his battle against cancer.
"Since then, his famous song has been sung at every single match, and in February this year a stunning tifo was displayed by Hammers fans in honour of the giant goalkeeper who will forever hold a special place in the hearts of the West Ham family.
"Everyone at West Ham United would like to extend their sincere condolences to Luděk’s family and loved ones at this very sad time."
His strong performances continued throughout his time in England, with Miklosko being named Man of the Match in West Ham's 1-1 draw against Manchester United on the final day of the 1994/95 campaign - a result that played a huge part in Blackburn Rovers clinching the Premier League title.
Miklosko's time at West Ham came to an end after a successful eight-year spell when he joined Queens Park Rangers, where he would continue playing until retiring in 2001.
Retirement led to a role as a goalkeeping coach with the Hammers, while Miklosko was most recently the sporting director for former club Banik Ostrava.