Mr Tamang is in Arunachal Pradesh to attend the swearing-in ceremony of Pema Khandu.
In a surprising move, Krishna Kumari Rai has quit as the MLA from Namchi Singhithang just a day after she took the oath of office. Ms Rai is the wife of Chief Minister Prem Singh Tamang, whose party, Sikkim Krantikari Morcha (SKM), swept the recent elections, winning 31 of 32 Assembly seats as well as the lone Lok Sabha constituency in the state.
Mr Tamang is in Arunachal Pradesh to attend the swearing-in ceremony of Pema Khandu, who is returning as chief minister.
Ms Rai, who was contesting the Assembly elections for the first time, had won with a margin of 5,302 votes. She had secured 71.6 per cent of the votes polled, second only to Chief Minister Tamang, who had got 72.18 per cent of the votes in Soreng-Chakung.
On Thursday, the chief minister's wife wrote a letter to her constituents explaining why she resigned, saying, in essence, that she had contested because she was honouring the party's decision.
"With a very heavy heart, I write to inform you that I have officially submitted my resignation... I had never imagined that I would enter electoral politics so soon... I have always viewed politics as a social activity, and the reason I entered the election was because I had to honour the decisions made by the parliamentary board and Party President," she wrote.
"I have always been a firm believer that, in order to serve the people, I do not need to hold a position. I have been helping and will continue to help from my own capacity. The Honourable Chief Minister and I assure that the new candidate for the Namchi Singithang constituency will be a committed and dedicated person who will serve the people of Namchi Singithang," Ms Rai added.
The chief minister's wife also praised her husband, stating that she was confident that Sikkim would be on the path of progress and development under his leadership.
Newly elected Speaker Mingma Norbu Sherpa, also from the SKM, has accepted her resignation.
Chief Minister Tamang said Ms Rai's resignation was "in alignment with the unanimous decision of the party" and that she had prioritised its "welfare and objectives".
The SKM chief also said that she had contested the election "at the request of the parliamentary committee" of the party. Assuring residents of Namchi Singhithang, he said he would ensure that the constituency "benefits from the care and attention of three representatives: the new candidate, Madam Krishna Rai, and myself".
"Please continue to have confidence in the leadership of the SKM Party, as well as in my personal care and concern for the people of the Namchi-Singithang constituency," he said.