St Johnstone winger Middleton and Celtic defender Welsh are due to meet at Hampden in the Premier Sports Cup semi-finals on Saturday.
Middleton's looked the more concerning injury, pulling up with no challenge as he stretched to bring down a high ball.
Welsh appeared to take a knock and limped off late on just before the visitors doubled their lead in the UEFA Under-21 Championship qualifier at Tannadice.
The centre-back started the previous two Celtic games before the international break with Carl Starfelt not assured of returning from a hamstring injury in time for Hampden.
The result left Scot Gemmill's side on four points from four matches while Group I leaders Belgium have won all six of their games.
Middleton had a good early chance after running on to Scott High's ball over the top, but fired just wide from inside the box.
Lois Openda dragged a similar chance well off target before getting the benefit of Josh Doig's poor touch and sending Yorbe Vertessen over the top. The striker volleyed over after goalkeeper Cieran Slicker came out to put him off.
Openda gave the Belgians the lead from the penalty spot five minutes before half-time. Hibs left-back Doig had been penalised for inadvertently catching Vertessen as he tried to clear following a pass in behind.
Lewis Mayo soon had a let-off when he pulled Openda down 22 yards from goal after losing the flight of a long ball, the referee handing out a yellow card as the visiting players called for a red.
The Scots had a decent spell around the hour mark with Lewis Fiorini sending a free-kick over before missing a great chance when he latched on to a short headed passback but could not beat the goalkeeper.
Slicker, another City player, then kept Scotland in it with three good saves before Adam Montgomery replaced Celtic team-mate Welsh in the 86th minute.
Welsh's absence was keenly felt within a minute when Nicolas Raskin ghosted in unmarked to meet a cross from the right wing and volley into the net from eight yards.