FIFA sends 'prayers' to Liverpool's Diaz after parents' kidnapping
Diaz's mother has been rescued but dozens of soldiers, backed by police, are searching for his father.
"On behalf of FIFA and the global football community, I would like to extend our support and prayers to Luis Diaz, his family and his friends in these difficult times," Infantino said on Instagram.
The Colombia football federation has also issued a further statement on X, formerly known as Twitter, demanding that those holding Diaz's father release him immediately, without conditions.
Liverpool manager Jurgen Klopp said after Sunday's 3-0 home win against Nottingham Forest that preparing for the game had been "the most difficult I've ever had in my life".
"I didn't expect that, I wasn't prepared for it," he added.
"I don't want to make the game bigger than it was, but definitely we tried to help Luis with the fight we put in because obviously we want to help and we cannot really help.
"So the only thing we can do is fight for him and that's what the boys did."
Liverpool's fifth straight home Premier League win of the season moved them three points behind leaders Tottenham.
Diaz, 26, who has made 11 appearances this season and scored three goals, did not feature in the squad.
Diogo Jota held aloft Diaz's number seven shirt after scoring in a tribute to his missing teammate.
"How can you make a football game really important on a day like this? It's really difficult. I've never struggled with that in my life," Klopp said.
"We heard late last night about it. We spoke to Luis, he wanted to go home. Then we got the news with his mum, which is fantastic, and since then nothing really."
The Colombian army said in a statement that it had set up roadblocks and deployed two motorised platoons, unmanned aircraft, helicopters and a plane with radar in the search for Luis Manuel Diaz.
Colombian authorities did not provide details about the kidnapping, but media reports said the player's father and mother, Cilenis Marulanda, were taken Saturday by armed men on motorcycles at a gas station in their home town of Barrancas, in the northern La Guajira department.
President Gustavo Petro said Marulanda was rescued in Barrancas hours later.
Colombia is a country just emerging from decades of civil conflict between rival armed groups, with more than 38,000 people kidnapped, mostly for ransom.
Petro, at an event to mark the start of local elections in Bogota, said "all the public forces have been deployed" to find Diaz's father.