Belarus state media said the aircraft – travelling from Athens in Greece to Lithuanian capital Vilnius – was switched to Minsk following a bomb threat.
Authorities in Minsk arrested activist and blogger Roman Protasevich – co-founder of the Nexta TV channel which was declared extremist by the authorities last year.
Mr Protasevich currently faces charges which could carry a prison sentence of up to 15 years.
Belarus state media said Mr Lukashenko personally ordered a MiG-29 fighter jet to escort the flight he was on to Minsk.
Officials said no explosives had been found on board while the deputy air force commander said the plane’s crew made the decision to land in the Belarus capital.
Mr Coveney said EU leaders need to make clear decisions following the incident, which opposition groups described as a “hijacking” of a plane.
“This was effectively state-sponsored aviation piracy,” Mr Coveney told RTE.
“It was an Irish airline, a plane registered in Poland, full of EU nationals, travelling between two EU capitals, flying through Belarusian airspace, which would be absolutely normal.
“It was intercepted, there was a warning given to the pilots and crew that there was a security risk on board and then the plane was escorted by a military jet to Minsk airport, which was not the closest airport.
“(The EU) needs to make some clear decisions that send a very strong signal to a regime in Belarus that has no democratic legitimacy and is behaving as a dictatorship, repressing their own people, expelling foreign journalists, silencing civil society and human rights defenders.”
Mr Coveney said the EU’s response has to be “clear, tough and happen quickly”, and that he supports the idea of closing Belarusian airspace.
“I think the sanctions need to be fully thought through in terms of consequences, but I think this is an incident that is on the upper end of the scale in terms of something that needs a very strong sanction-based response.”
Mr Coveney said that while he did not know whether there were KGB officials travelling on the plane, he said five or six people got off and did not reboard after it landed.
Leaders from the European Union will hold emergency talks to discuss the situation.
Foreign Secretary Dominic Raab hinted at tougher action from the UK.
Mr Raab said he was working with allies on a coordinated response, stating that Mr Lukashenko must be held to account for his “outlandish actions”.
Mr Raab said: “The UK condemns yesterday’s actions by the Belarusian authorities, who arrested journalist Roman Protasevich on the basis of a ruse, having forced his flight to land in Minsk.
“Mr Lukashenko must be held to account for his outlandish actions.
“The UK calls for the immediate release of Mr Protasevich and other political prisoners held in Belarus.
“The UK is working with our allies on a coordinated response, including further sanctions.”
He said the International Civil Aviation Organisation’s council should hold an urgent meeting to consider the regime’s flouting of the rules.
The Foreign Secretary will update MPs on the situation on Monday afternoon.