Pranab Mukherjee, the foreign minister, is expected to stand in as prime minister while Singh is absent from duty for three weeks of rest.
Mukherjee may also preside over India's Republic Day ceremonies on Monday.
Singh is due to lead the Congress party into general elections in May, but fears over his health could undermine a re-election campaign.
The prime minister has had a history of heart problems.
Singh underwent bypass surgery in 1990 in the UK, and had an angioplasty in 2003.
Officials said he also underwent wrist surgery in 2006, prostate-gland surgery and a cataract-removal procedure last year.