It is the end of a trophy-less 18 months in charge for Neeskens, a former assistant coach with the Netherlands, Barcelona and Galatasaray.
Sundowns have struggled all season despite having the most expensive squad in the league.
They have won twice in 12 league games and are second from bottom. Neeskens's team also lost 1-0 to Bloemfontein Celtic in Saturday's League Cup final.
The club said he would be replaced by former South Africa coach Pitso Mosimane who was responsible for a blunder that led to the country failing to qualify for the 2012 African Nations Cup finals.
Mosimane misunderstood the permutations on the final day of the campaign and ordered the team to play for a draw in their last qualifier when they needed a win.
Neeskens played at the 1974 and 1978 World Cups, scoring a penalty in the 1974 final when the Dutch were beaten 2-1 by hosts West Germany.
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- Bloemfontein Celtic