Brindisi, a former Huracan, Las Palmas, Boca Juniors and Argentina midfielder, had been in charge since September, eight matches into the Apertura which is the first of two championships in the 2010/11 season.
"We didn't expect this news and we're hurt because Miguel is part of the Huracan family and we had a lot of faith in his project," club vice-president Norberto Giuliano told ESPN Radio.
"Although the results did not come, we believed the situation could be reversed and we accepted that we could lose the match with River."
Brindisi, who has won titles as a coach with Barcelona of Ecuador and Argentina's Independiente, steered a young Huracan side to a promising 3-0 home win over arch-rivals San Lorenzo in October but they have since won only one match in nine and are in serious danger of relegation.
In the points averages over three seasons that are used to determine relegation from the Argentine first division, Huracan are three from bottom facing a play-off with a Nacional B (second tier) team.
Huracan were second in the 2008/09 Clausura championship but did not save coach Angel Cappa, who had forged a brilliant team in one season at the club. He was replaced by Hector Rivoira whose resignation in September opened the door for Brindisi.
Brindisi and Huracan president Carlos Babington were midfield partners in the 1973 league title-winning Huracan side and the Argentina team at the 1974 World Cup in West Germany. He also won a title as captain of Diego Maradona's Boca in 1981.
