Both punishments were doled out as the result of actions in last week's Houston/Seattle match.
Moffat was punished for a reckless challenge on Seattle midfielder Osvaldo Alonso in the 35th minute of last Friday's encounter, which the Sounders won 2-0.
Fernandez received his fine for embellishment of contact in the 82nd minute of the same match. He received a yellow card during the game for simulation.
The punishments aren't the first to come from this match, as earlier in the week Dynamo midfielder Colin Clark was suspended three games and fined an undisclosed amount for shouting a homophobic slur at a Seattle ball boy.
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