Morrison's conservative government argues that the bill, passed 75 to 74 by the House of Representatives on Tuesday, will undermine Australia's tough refugee policy.
"I just say to people trying to put out the welcome mat for people smugglers, the medivac legislation applies for people who are already there, it does not apply to anyone new", he told reporters.
Mr Morrison said he expected the new medical evacuation laws could restart the people smuggling trade and Australia needed to be ramp up national security efforts as a result.
Mr Morrison lost his parliamentary majority a year ago and has been relying on cross-benchers to keep control of the Lower House of Representatives. He has ruled out calling a snap election on the refugee issue.
Prime Minister Scott Morrison said a security committee of his cabinet agreed to reopen the camp on Wednesday on the advice of senior security officials.
Constitutional expert Anne Twomey, a professor of law at the University of Sydney, said the Solicitor-General's opinion was "pretty fair and accurate" but that the final decision was up to the Parliament itself, with completely different views on section 53 between the two chambers.
Sick asylum seekers often have to fight the Australian government in court for permission to be transferred to an Australian hospital.
Professor Twomey said that if the government claimed the bill was a money bill, the government would be exposed to claims it should lose power if it lost a vote on the bill.
"See, for example, the fall of the Fadden government in 1941 when the budget was amended to reduce it by the nominal sum of one pound".
The Bill passed with the support of the main opposition Labor Party and cross-benchers from the left-leaning Greens and independent MPs.
He said he was confident anyone who was transferred to Australia would remain in detention while receiving treatment.
Speaking in front of Parliament House this morning, Morrison reiterated his position the vote will encourage people smugglers to continue their operations in Australian waters - and that reopening the shuttered centre was part of a contingency plan to dissuade those potential arrivals.
Labor is also pushing major reforms to the health system.
When he announced his decision, Mr Hinch said it was the hardest vote he had cast in the Upper House.
Then it's up to the minister to reject it on medical grounds again, or national security grounds, or if the person has a substantial criminal record and poses a threat to the Australian community.
David Crowe is Chief Political Correspondent of the Sydney Morning Herald and The Age.