Mr Trudeau underscored his government’s commitment to bringing in “those fleeing persecution, terror & war”.
The US Department of Homeland Security said the entry ban would also apply to dual nationals of the seven countries.
However, Mr Trudeau’s office says Canadian dual nationals are exempt.
“We have been assured that Canadian citizens travelling on Canadian passports will be dealt with in the usual process,” a spokeswoman for Mr Trudeau said in an emailed statement.
US President Donald Trump’s National Security Adviser Mike Flynn “confirmed that holders of Canadian passports, including dual citizens, will not be affected by the ban,” the statement said.
Canada’s Immigration Minister Ahmed Hussen is a dual national who arrived as a Somali refugee.
Within hours, Mr Trudeau’s tweets had been shared more than 150,000 times.
“Welcome to Canada” also became a trending term in the country.
— Justin Trudeau (@JustinTrudeau) January 28, 2017
Mr Trudeau, who gained global attention for granting entry to nearly 40,000 Syrian refugees to Canada over the past 13 months, also sent a pointed tweet that showed him greeting a young refugee at a Canadian airport in 2015.
On Friday, Mr Trump signed an executive order suspending entry to the US from Iraq, Syria, Sudan, Iran, Somalia, Libya, and Yemen for 90 days.
The US’s entire refugee admissions programe has also been suspended for 120 days. Those fleeing Syria as refugees are banned until further notice.
The executive orders created confusion in airports around the world as immigration and customs officials struggled to interpret the new rules.
The Canadian government is also in contact with the US administration “to get more clarity” on how the executive orders will affect Canadians citizens travelling to the US, said federal Transport Minister Marc Garneau.
On Saturday, the US State Department confirmed to the BBC that all travelers – including those with dual nationality – from one of the seven designated countries will be barred from entering the US.
That includes people with valid immigrant or non-immigrant visas.
Mr Trudeau has refrained from criticizing Mr Trump, despite the fact the two leaders have divergent political views.
In recent media appearances, the prime minister has focused on the long friendship between Canada and the US and the deep economic ties between the two nations. The US is Canada’s primary trading partner.
Canada plans to allow 300,000 immigrants into the country in 2017, mostly through economic immigration, though that figure includes 40,000 refugees.