Sharif was due to visit Washington to participate in the fourth Nuclear Security Summit (NSS) on March 31 hosted by US President Barack Obama.
"Prime Minister Nawaz Sharif has cancelled his upcoming visit to the United States," Radio Pakistan tweeted minutes before Sharif's address to the nation.
At least 72 people, including 29 children, were killed and 233 were injured in a blast near Gulshan-e-Iqbal Park in Lahore on Easter Sunday.
Special Assistant to the Prime Minister on Foreign Affairs will now represent the premier at the crucial global event, Express News reported.
According to media reports, Sharif and Prime Minister Narendra Modi were likely to meet on the sidelines of the Summit.
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Sharif's surgery will be conducted at London's The
Princess Grace Hospital, which is considered one of the best-equipped multi-disciplinary hospital in the UK capital.
Sharif, who is in London, has been facing pressure from Opposition political parties at home to conduct a thorough investigation into the Panama Papers leaked documents - that reveal that members of his family own undeclared offshore wealth and expensive property in London.
The Opposition has been demanding Sharif face parliament and respond to various questions regarding how his family transferred money from Pakistan to set up businesses abroad.
According to the leaked documents, Sharif's children owned at least three offshore holding companies registered in the British Virgin Islands.
Sharif and his family have denied any wrongdoing.