Xavier Bettel addressed the media alone, next to an empty podium, after the two leaders held talks following a meeting between Mr Johnson and the EU Commission President, Jean-Claude Juncker.
Both European leaders said the UK had yet to present any concrete proposals for resolving the problem of the Irish border after Brexit, and Mr Bettel warned that time was running out to find an alternative before the 31 October deadline.
Referring to the protesters - British citizens living in Luxembourg - Mr Bettel said: "Our people need to know what is going to happen to them in six weeks' time. They need clarity, they need certainty and they need stability.
"You can't hold their future hostage for party political gains."
Gesturing to the empty podium where Mr Johnson should have been, the Luxembourg Prime Minister added: "Now it's on Mr Johnson - he holds the future of all UK citizens and every EU citizen living in the UK in his hands.
"It's his responsibility. Your people, our people, count on you - but the clock is ticking, use your time wisely."
Mr Johnson decided to only give a statement to a small group of journalists assembled at the nearby residence of the British ambassador. A Downing Street source was quoted saying that the Prime Minister offered to hold a press conference indoors, but his hosts declined.