The Torreon-based club announced on Wednesday morning that the playing staff had undergone COVID-19 tests during this week as a precaution before a possible return to training.
"Eight players received positive results for COVID-19," read a statement from Liga MX on Wednesday evening. "However, they are asymptomatic."
Plans for Liga MX to resume, possibly by playing the games in one city, had been floated by Chivas earlier this week, but that now seems unlikely.
"This goes beyond us, the talks we have had with clubs were about how we can return as soon as possible," Santos owner Alejandro Irarragorri told TUDN Wednesday evening. "This situation complicates the return in a big way."
Irarragorri confirmed that a total of 48 people at Santos Laguna had been tested and that only 22 of the tests have come back so far, raising the prospect of more possible positive results.
"It's a bucket of cold water in every way," continued Irarragorri, who said the situation about a potential return is still fluid.
There had been a growing consensus among Liga MX clubs that it would be prudent to cancel the 2020 Clausura season and focus on starting the 2020 Apertura on time in mid-to-late July, with a decision expected in coming days.
The numbers of COVID-19 cases in Mexico rose by 2,248 to 56,594 between Tuesday and Wednesday, with deaths increasing by 424 to 6,090, according to government figures.
The Mexico City government announced on Wednesday that the earliest sports could return on June 15, but that will depend on a drop in the number of cases in each state.