Sala, 28, was one of two people on a light aircraft travelling from Nantes to Cardiff, having agreed a £15m transfer from the Ligue 1 club last Saturday.
With the aircraft expected to land on Monday evening at 9pm, suspicion aroused when it failed to arrive and the Argentine striker failed to respond on social media.
— ITV Wales News (@ITVWales) January 22, 2019
Cardiff chief executive Choo released a statement that read: "We were very shocked upon hearing the news that the plane had gone missing. We expected Emiliano to arrive last night into Cardiff and today was due to be his first day with the team.
"Our owner, Tan Sri Vincent Tan, and chairman, Mehmet Dalman, are all very distressed about the situation.
"We made the decision first thing this morning to call off training with the thoughts of the squad, management staff and the entire Club with Emiliano and the pilot.
"All of us at Cardiff City FC would like to thank our fans, and the entire footballing family for their support at this difficult time.
"We continue to pray for positive news."
He added on Sky Sports News; "When we get some news then we will convey it from the club.We have a lot of fans and supporters who are concerned and we understand, and we are concerned too.
"We are waiting for them to inform us. We are trying to communicate to the agent of the player, to his family as well.
"At this point in time we just want to know if he is ok, if the pilot is ok and if the plane is ok."
The player, who was signed to lead the Bluebirds charge of relegation, netted 13 goals in 21 games for Nantes across all competitions this season.