The experienced doubles pair were eliminated by fellow Australians Jaimee Fourlis and Andrew Harris 6-4 7-6 (8-6).
Wildcards Fourlis and Harris progress to the quarter-finals, where they will meet fifth seeds Laura Siegemund and Sander Gille.
After securing the match-winning point, Fourlis gasped and put a hand over her mouth in shock.
They are one of two Australian pairs in the last eight, with fellow wildcards Olivia Gadecki and Marc Polmans advancing after a tough second-round match against Michael Venus and Aldila Sutjiadi.
The result comes three days after Hunter's brave run in the singles ended when she lost in the third round against former French Open champion Barbora Krejcikova in three sets.
But Hunter remains in contention to secure a maiden title at Melbourne Park after reaching the quarter-finals of the women's doubles.
Hunter, who is third seed with Katerina Siniakova, will face Krejcikova again.
Krejcikova and Siegemund are the fifth seeds and will prove a tough contest for Hunter and Siniakova.
It is Hunter's third straight appearance in a quarter-final at Melbourne Park, but she has never progressed any further in the women's doubles.
However, she reached the semi-finals in the mixed doubles in Melbourne in 2021.
In 2022, she partnered fellow Australian John Peers to be crowned US Open mixed doubles champions.
Ebden is the only Australian left in the men's doubles after he and 43-year-old Indian partner Rohan Bopanna advanced to the quarter-finals.
The second seeds will take on Argentine duo Andres Molteni and Maximo Gonzalez in the final eight.
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