Mikloško started his career in his native Czechoslovakia with Baník Ostrava. His talent was noted by West Ham United manager Lou Macari, who signed him on 19 February 1990, just before his resignation and the appointment of Billy Bonds as his successor, for a fee of £300,000.
A brave and excellent shot stopper with a huge clearance kick, he went on to play 374 times for the team. He was named Hammer of the Year in 1991 - the year that West Ham were promoted to the First Division as Second Division runners-up and reached the FA Cup semi-final. Although the Hammers were relegated the following season and missed out on being founder members of the new FA Premier League in 1992, he helped them win promotion back to the top flight at the first attempt - beginning a 10-year unbroken spell at this level, although during Miklosko's time at the club they never finished higher than eighth (in his final season). He is well remembered for a man of the match performance against Manchester United on the last day of the 1994–95 season where West Ham drew 1–1 with Manchester United to help secure Blackburn Rovers their first league title in over 80 years.
He was eventually sold to Queens Park Rangers in 1998 for a nominal fee after a successful loan spell. He retired due to injury in 2001.