"Despite the best efforts of the phenomenal staff at Chur hospital, Gino couldn't make it through this, his final and biggest challenge, and at 11:30 a.m. we said goodbye to one of the shining lights of our team," the team said.
Mader crashed on the descent towards La Punt and fell into a ravine where he was found unresponsive by the race doctor and resuscitated before being air-lifted to hospital.
Ineos Grenadiers rider Magnus Sheffield was also injured in the crash and taken to hospital with concussion and soft tissue damage, according to his team.
In a Bahrain Victorious statement, team managing director Milan Erzen said: "We are devastated by the loss of our exceptional cyclist, Gino Mader. His talent, dedication, and enthusiasm were an inspiration to us all.
"Not only was he an extremely talented cyclist, but a great person off the bike. We extend our deepest condolences to his family and loved ones, and our thoughts are with them during this difficult time."
Erzen said the team would continue in the race in honour of Mader.
"We are determined to show the spirit and passion Gino displayed, and he will always remain an integral part of our team," he said.
Mader joined the Bahrain Victorious team in 2021 and won a stage of the Giro d'Italia that year. He also won the young rider classification at the 2021 Vuelta a Espana.
'OUR HEARTS BLEED'
A statement from the professional riders' association CPA, read: "Our hearts bleed at this news. Condolences to his family, the team and the many friends who loved him.
"Like all of us. RIP Gino."
Stage five of the Tour de Suisse had raised some eyebrows in the peloton because of its fast descent near the finish.
After the accident, Belgium's world champion Remco Evenepoel said on Twitter: "I hope that the final of today's stage is food for thought for both cycling organisers as well as ourselves as riders.
While a summit finish would have been perfectly possible, it wasn't a good decision to let us finish down this dangerous descent."
Mader's death brought back memories of a Belgian rider who died following a crash during a descent on the third stage of the 2011 Giro d'Italia.
Weylandt, who was 26, fell off his bike coming down from the Passo del Bocco and suffered multiple injuries including to his skull.
Doctors at the scene cut off Weylandt's helmet and performed cardiac massage for 45 minutes at the side of the road but their efforts were in vain.