In videos of the incident posted on social media, Guzman, who was injured and sitting in the stands, could be seen directing the laser pointer at the Monterrey players including Andrada in the match, which ended 3-3.
Guzman later issued an apology.
The FMF said in a statement from its disciplinary commission on Thursday that the sanctions should "mark a before and after" in Mexican football.
"This commission has resolved to sanction Nahuel Ignacio Guzman Palomeque of Club Tigres with an 11-match suspension, an economic fine and hours of social work," the governing body added.
In a statement on their website, Tigres accepted the punishment and added that they would further discipline Guzman.
The federation also fined Andrada for a social media post in which he insulted Guzman using a homophobic slur.
