MLS launched an investigation after the Frisco Police Department received a report that the 25-year-old was involved in incidents of domestic abuse in the Dallas suburb.
A statement from the league read: "MLS is conducting an independent investigation into the matter and will remain in close communication with FC Dallas, local law enforcement, and the MLS Players Association throughout the process.
"Gonzalez proactively submitted to, and is currently undergoing, an assessment by Substance Abuse and Behavioral Health (SABH) doctors. Gonzalez will not be eligible to participate in any team activity until the assessment is complete, he is cleared for participation by the SABH Program doctors and Major League Soccer completes its investigation."
FC Dallas said they learned of the allegations earlier this week, adding that they support the league's decision to suspend Gonzalez.
Gonzalez appeared in the club's first two matches of the season before play was halted in March due to the coronavirus pandemic. Last season, he started 33 matches and kept eight clean sheets.