Eta has been put in charge in an interim role for the team's final five games of the Bundesliga season to secure their status in the top-flight.
She replaces Steffen Baumgart, who was fired with his assistants Danilo de Souza and Kevin McKenna after the team's 3-1 loss at bottom side Heidenheim on Saturday.
Union Berlin are currently 11th in the Bundesliga standings, seven points clear of St. Pauli in the relegation zone with five games remaining.
"I'm delighted that Marie Louise Eta has agreed to take on this role on an interim basis before she becomes head coach of the women's first team as planned in the summer," Union sporting director Horst Heldt said in a statement.
Eta added: "Given the points gap in the lower half of the table, our place in the Bundesliga is not yet secure.
"I am delighted the club has entrusted me with this challenging task. One of Union's strengths has always been, and remains, the ability to pull together in such situations.
"I am convinced that we will secure the crucial points."
Real Madrid were left furious after a dramatic late collapse saw them knocked out of the UEFA Champions League by Bayern Munich, with manager Alvaro Arbeloa insisting a controversial red card "ruined" the tie.
Harry Kane hailed Luis Diaz after his late goal capped a dramatic night as Bayern Munich beat Real Madrid 4-3 to reach the UEFA Champions League semi-finals with a 6-4 aggregate win.
Real Madrid midfielder Jude Bellingham believes his team need to be aggressive in order to turnaround the UEFA Champions League second leg fixture at Bayern Munich on Wednesday.
Vincent Kompany has insisted Jamal Musiala is firmly on the right path despite not yet reaching his peak, after the midfielder delivered a standout performance in Bayern Munich's recent dominant 5-0 win over St. Pauli.
