The program is once again compliant with national guidelines, but still has to improve its documentation practices, she said in a statement.
On Wednesday, the Department of Health announced it was temporarily suspending the program for up to two weeks to make some interim changes after a Health Canada inspection on July 6 found "several problems" with the way the program collects and manages it documentation.
In one case, for example, "a piece of necessary information" was not obtained from a donor who had a tattoo, Dubé had said.
Donors with tattoos are required to go through additional screening before their organs can be cleared for donation due to the potential health risks that may be involved in the tattoo procedure.
"It was this case that resulted in the province's non-compliance rating and led to the province's decision to suspend the program," said Dubé.
But on Thursday, Health Canada inspectors and scientific advisers reviewed the case during a national teleconference, she said.
"It was decided that the province was still acting within the regulations even if some of the information about the tattoo was not collected."
Health Canada also examined the work completed since July 9 to address the identified gaps and "was reassured by New Brunswick's commitment to improve its documentation practices and to implement a quality assurance program by this fall," the minister said.
Dubé said she is "relieved" the program did not have to refuse any organ donations during the week the program was suspended.
Health Canada usually inspects provincial organ donation programs every two years.