I'm looking for the same question, and seems there are no clarity.
I hope someone could give us.
See, for instance, what Levelt state in his book ("An Introduction to the Theory of Formal Languages and Automata" Cap1, p. 1):
From a mathematical point of view, grammars are FORMAL SYSTEMS, like Turing machines, computer programs, prepositional logic, theories of inference, neural nets, and so forth. 
Despite of this, it's a really matter whats others answers pointed out here, because formal grammars seems truly miss some fundamental attributes (i.e. deductive apparatus) to be marked as formal systems.
However, if a Turing machine is a formal system , and formal languages (and its representations, grammars) are equivalents to them: why grammars is not a formal system too?
I hope this consideration, event though are not conclusive may animate some improved answer to this problem.