The Tottenham defender is the eighth absentee for Belgium, with Yannick Ferreira Carrasco, Christian Benteke, Kevin De Bruyne, Eden Hazard, Vincent Kompany, Divock Origi and Jan Vertonghen already ruled out.
Wilmots may subsequently use versatile Nantes midfielder Gillet in place of Alderweireld, but would not reveal precise details on how his side will line up for the match in Leiria.
"Guillaume has never disappointed, he was still doing well at right-back with Anderlecht and currently plays with great confidence," said the coach.
"So much has happened during the last days. Players could still fall sick or get injured, so we will consider the team tomorrow – and I do not want to give the opposition an advantage."
Despite his lengthy injury list, Wilmots is remaining positive and hopes to see the fringe players take their chance with Euro 2016 just around the corner.
"The result is not the most important thing tomorrow, but the manner of our play. I want to see discipline, a collective block and good pressing. The solidity of the team interests me," he added.
"We are missing some important players, but that's not an excuse for us. Those who have played less have the opportunity to show themselves.
"We should not weep for the many injured players. If there is a problem, we find a solution. Belgium does not want to lose, Belgium wants to win."
The Belgium coach also highlighted the threat of Cristiano Ronaldo, who he feels just needs an international title with Portugal to complete a decorated career.
"He is a player who was once considered the best in the world. He is a player who scores 45 goals per season," Wilmots continued.
"He has won everything there is to win at club level; he is just missing something with the national team."
Former Benfica midfielder Axel Witsel will captain Belgium in Leiria and insists they will not be focused on trying to nullify Ronaldo.
"He's one of the best players in the world, but Portugal has other good players in attack like Quaresma, Nani and Danny. There will not be anti-Ronaldo tactics," he said.