The clash came at an otherwise congratulatory press conference following the first meeting of foreign ministers of the EU's new Eastern Partnership initiative.
The focus of the diplomatic spat was Tatsyana Shaputska who, according to Belarus opposition supporters, was thrown out of the Belarusian State University after taking part in a Civil Society forum on the Eastern Partnership in Brussels last month.
"If it is the case that one is thrown out of university just because of participation in this civil forum then that is of course unacceptable in every single way," Bildt said.
At that point Belarus Foreign Minister Sergei Martynov chimed in to defend his country's stance.
"Governments do not expel students, it's universities that expel them," he assured.
"The university quoted us her absenteeism," he added.
Bildt was not going to let that comment go unchallenged.
"Although of course it was said that the university had been contacted by state security bodies," he reminded the assembled ministers and journalists.
"It might be that state security bodies were concerned with absentee rates but that is not normally what state security bodies do," he added.
His Belarusian counterpart remained silent at this stage.
The EU launched the Eastern Partnership at a summit in Prague in May to "accelerate political association and further economic integration" between its 27 member states and Armenia, Azerbaijan, Belarus, Georgia, Moldova and Ukraine.
Last month European Union nations agreed to seek improved ties with Belarus, deemed the democratic laggard of the group, and refrained from enforcing a travel ban on its leaders.
The move is subject to Belarus improving democracy, human rights and the rule of law, as the EU strives to keep pressure on Belarus President Alexander Lukashenko -- once dubbed "Europe's last dictator" by the United States.
Lukashenko has ruled the ex-Soviet republic of 10 million people since 1994 but has now made attempts at greater openness -- including the hiring of a Western PR firm and cautious economic reform.