The 29-year-old Ferencvaros striker was given the nod up top for the third time at the Championships in Sunday's Group A finale against Scotland, seeking to build on the consolation goal he netted against Switzerland on the opening matchday.
However, Varga was involved in a sickening collision with Scotland goalkeeper Angus Gunn in the second half, as the latter clattered into the Hungary striker when coming out to meet a free kick.
Varga immediately dropped to the turf and sparked huge concern from his teammates, who hurried medical staff onto the field while a curtain was put up around their stricken compatriot.
The Varga incident evoked memories of Christian Eriksen's harrowing collapse at Euro 2020, where his fellow Denmark players formed a protective shield around him while medics tried to resuscitate him, and play was halted for several minutes while Varga received treatment.
Rossi provides Varga update after horror injury
The 29-year-old was eventually stretchered off the field to warm applause from the entire stadium, and he was subsequently confirmed to be stable and conscious in a Stuttgart hospital.
Hungary then revealed that Varga had sustained a number of facial fractures as well as a concussion, and he would "most likely" undergo an operation after spending the night in hospital.
Following Varga's distressing injury, Hungary dramatically edged out Scotland 1-0 courtesy of a last-gasp Kevin Csoboth winner to finish third in Group A, potentially enough for a place in the last 16.
As expected, though, Hungary head coach Rossi has confirmed that Varga's tournament is over, and the striker will not play in any knockout ties if the Magyars make it that far.
"Barnabas Varga's life is not in danger. He will undergo an operation after fracture in his face and he won't be available for the rest of Euro 2024," Rossi told the media.
After eliminating Scotland in the most remarkable of circumstances and keeping their Euro 2024 dreams alive for the time being, Hungary players paid an emotional tribute to Varga, holding up a shirt with the forward's name on it.
Who could Hungary face in Euro 2024 last 16?
As things stand, Hungary will make it through to the knockout stages of Euro 2024 as one of the best third-placed sides, having accrued three points from their nine matches in Group A.
Before Monday's Group B fixtures kick off, Slovenia (Group C), Austria (Group D) and Slovakia (Group E) are also on course to reach the last 16, with Albania (Group B) and the Czech Republic (Group F) missing out.
As a result, Rossi's men are currently due to take on Portugal - the victor of Group F - although they could also end up facing the winners of Group E or B if the third-placed rankings change.
Spain have already been confirmed as Group B winners, while all of Romania, Belgium, Slovakia and Ukraine are level on three points in Group E.