Katherine d'Entremont recommends the change take effect in 2020 in her annual report released Thursday.
Currently, 50 per cent of senior officials in government departments and agencies are able to perform their duties in both English and French, she said.
"Given the nearly 50 years since the adoption of the first Official Languages Act, how is it that all of our senior public servants are not bilingual?" she asked.
In the meantime, she recommended that any unilingual person in a senior position be required to attain an advanced level of proficiency in the other official language.
New Brunswick is Canada's only officially bilingual province.
Senior public servants, such as deputy ministers, assistant deputy ministers and executive directors, account for about three per cent of all government employees.
D'Entremont said people in the senior positions must be able to communicate with the public in both English and French and supervise both anglophone and francophone employees.
But Donald Arseneault, the minister responsible for official languages, said he's not going to order such a policy.
"We have some tremendous people in the civil service that are unilingual francophone and unilingual anglophone and they provide great service to the public in New Brunswick," he said.
"I want to make sure that everybody has an opportunity but it's not by implementing such policies that we'll see that happen."
Arseneault said language training is available to staff.
D'Entremont also recommends legislation requiring bilingualism for the eight officers of the legislature, such as the ombudsman and the access to information and privacy commissioner.
But Arseneault said he won't bring forward such legislation.
D'Entremont said the City of Miramichi has failed to comply with its language obligations for several years and she called on the government to ensure the municipality complies with the Official Languages Act.
She said it's a difficult situation because there are no sanctions or fines under the law that requires Miramichi to comply.
Arseneault said he wants to sit down with the council in Miramichi to see how the province can work with them to meet their language obligations.