He was awarded the Gunnerus Medal in 1930, and in 1943 a "Headmaster Qvigstad's Gold Medal" was inaugurated by Tromsø Museum. He was decorated as a Commander with Star of the Royal Norwegian Order of St. Olav in 1912, and as a Commander of the Order of the White Rose of Finland.
He was a member of the Société Finno-Ougrienne from 1885, the Norwegian Academy of Science and Letters from 1888 and the Royal Norwegian Society of Sciences and Letters in 1894. He was an honorary member of the Société Finno-Ougrienne from 1910 and Tromsø Museum from 1926, and Festschrifts were issued for his 75th and 100th birthdays.