Seats in the seven-member government, known as the Federal Council, are distributed among Switzerland's four main parties, and rarely shift hands.
But with current President Alain Berset due to step down at the end of the year, parliament will vote in a new government member and portfolios could be shuffled around. Berset also serves as health minister.
The Swiss presidency rotates annually among the seven ministers, and Amherd, 61, is next in line.
Barring a major upset, she should be picked to take on the role of president starting on January 1.
Amherd, a member of The Centre party, is a lawyer from the southern canton of Wallis with a reputation for being discrete but also doggedly determined.
Proudly single, she was largely unknown to the public before entering government in 2019, when she replaced a departing defence minister and thus became the first woman to hold that position.
She quickly gained respect among her colleagues, other political parties and the public, with a recent opinion poll indicating she is considered the most hard-working of the government ministers.
Amherd has secured a number of political successes since the start of Russia's war in Ukraine, including gaining acceptance for significant hikes to the Swiss defence budget and convincing parliament to pick US-made F-35 fighter jets as Switzerland moves to replace its fleet.
- Magic formula -
In addition to voting Amherd into the presidency, Switzerland's 246 parliamentarians are expected to elect the six other government members on Wednesday.
Six of those seats are most likely to be filled by their current occupants, with one seat up for grabs.
Under a tacit, decades-old agreement dubbed the "magic formula", the seven ministerial posts in the executive branch are shared among Switzerland's major parties.
The system ensures that the cabinet reflects views from across the political spectrum and the executive has generally remained unaffected by power-balance shifts in parliament.
Swiss general elections in October, which further bolstered the extreme right-wing Swiss People's Party (SVP) -- already the country's largest political party -- is thus not expected to have any bearing on the government makeup.
The SVP holds two government seats, as does the Socialist Party and the Liberals, while the Centre has one.
Berset's looming departure leaves one seat to be filled.
His Socialist Party has proposed two candidates to replace him: Beat Jans, a 59-year-old environmental scientist, and Jon Pult, a 39-year-old dual Swiss-Italian national and historian by training.
The parliamentarians are also expected to select Finance Minister Karin Keller Sutter to serve as Swiss vice president next year, putting her in line to take over the presidency in 2025.
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