It’s perfectly safe to put your mattress on plywood – whether it’s raw or covered with fabric. There are only two issues you might encounter: damage to your mattress and airflow issues.
A raw sheet of plywood may have rough edges and splinters that could snag and tear at your mattress, not to mention your sheets and skin. If possible, try to sand the plywood sheet and cover it with fabric beforehand, or use a plywood bunkie board.
Also, a plywood sheet may prevent your mattress from breathing. This can easily be fixed by using plywood slats or planks. Make sure they’re secured so they don’t slip off or move around!