In a statement Huonder's diocese said under ecclesiastical law a bishop who has reached the age of 75 must offer his resignation to the Pope.
The diocese will not make any further comment until the Pope has made his decision.
Huonder has long provoked controversy in Switzerland due to his ultra-conservative views.
In 2011 he came under fire for arguing that parents should have the right to exempt their children from sex education at school.
At the time he said “state institutions promote a kind of education that destroys the natural protection of a person's sexuality, namely the sense of shame”.
In 2015 he called on a catholic priest in the canton of Uri to step down for conducting a blessing for a lesbian couple. Huonder said the priest had upset many people, despite the fact the priest's village backed him and started a petition in his defence.
Later that year Huonder provoked a media storm when, at a debate on marriage and family, he quoted passages from the Bible that condemn homosexuals to death.
Swiss gay rights organization Pink Cross demanded an apology from the bishop and filed criminal charges against him for ‘inciting people to crimes' with his words.
Huonder did then apologize, saying the speech was a “mistake” and he should have asked colleagues to read it before going ahead.
The criminal charges against Huonder were later dismissed by a Graubünden court, and again on appeal, with Pink Cross ordered to pay court costs.