The departure of the top judge, Sylvere Nimpagaritse, on Monday came hours after at least three people were killed during anti-Nkurunziza protests in Burundi's capital, Bujumbura. Clashes between police and demonstrators over the past nine days have left at least nine people with at least another 600 arrested.
Nimpagaritse told AFP news agency that he fled on Monday due to the "enormous pressure and even death threats" from senior figures to rubberstamp the disputed candidature of the former rebel leader.
On leaving the country, the Burundi judge claimed a majority of the court's seven judges believed it would be unconstitutional for Nkurunziza to stand again.
Presidents in Burundi are constitutionally barred from seeking a third term in office. Nkurunziza supporters say he is eligible for a third term, however, because he was elected president for his first term in 2005 by law makers and not by popular vote.
Burundi's ruling CNDD-FDD party announced on Saturday that Nkurunziza would be their candidate in June's presidential poll, with the president calling on people "to go to the election in peace."
"But I would like to warn everyone: whoever wants to create problems with the ruling party elected by the people, he'll find himself in trouble," Nkurunziza said.
Peace deal at risk
The president's nomination has been criticized by opposition leaders and international figures alike.
Ahead of the announcement on Saturday, opposition leader Agathon Rwasa implored Nkurunziza not to seek a third term in office, warning that such an attempt would destabilize the country and threaten to reignite tensions stemming from a 13-year civil war between Tutsis and Hutus which ended in 2005.
US Secretary of State John Kerry also warned on Monday that he was "deeply concerned" about Nkurunziza's decision to stand again, which he said "flies directly in the face of the constitution."
According to the United Nations (UN), thousands of people have already fled Burundi to neighboring Rwanda and the Democratic Republic of Congo to escape the violence.
ksb/bk (Reuters, AP, AFP, dpa)