Transport Minister Khaw Boon Wan will be undergoing surgery on his fractured left arm tomorrow.
Mr Khaw, 66, thanked well-wishers in a Facebook post yesterday, adding that he was fully prepared for the upcoming surgery.
He said he would have to be patient in convalescing, as "the bones' recovery can take several weeks".
"I'm in the best of hands and looking forward to a full recovery," he added.
Mr Khaw is warded in Singapore General Hospital.
In his post, Mr Khaw said his accident at home was a timely reminder that it was important for senior citizens to "never jump out of bed".
"At our age, it's important to get up, pump the heart, stand up, feel that you are steady before taking the first step," he said.
The Prime Minister's Office (PMO) said on Monday that Mr Khaw was on extended medical leave after fracturing his left arm in a fall last week.
He will resume duties when he is able to do so, probably after several weeks, the PMO said in a statement.
Foreign Minister Vivian Balakrishnan, 58, has stepped in as Acting Transport Minister while Mr Khaw recovers from his injury, to ensure that ongoing discussions with Malaysia on several transport matters will continue to be well coordinated, the statement added.
On Monday, the PMO said that senior ministers of state for transport Lam Pin Min and Janil Puthucheary, together with Senior Parliamentary Secretary for Transport Baey Yam Keng, will help Dr Balakrishnan in the parliamentary debate on the spending plans of the Transport Ministry.
The other MPs in Mr Khaw's Sembawang GRC will be covering his duties in the constituency.
Senior Parliamentary Secretary for Home Affairs and Health Amrin Amin, one of his fellow Sembawang GRC MPs, was at Mr Khaw's Meet-the-People session on Monday evening.
Mr Vikram Nair will be covering next Monday's session.