NFL quarterback Tarvaris Jackson will NOT be prosecuted for allegedly pulling a loaded gun on his wife and threatening to shoot her ... TMZ Sports has learned.

33-year-old Jackson was initially charged with aggravated assault with a deadly weapon after he allegedly pointed a loaded gun at his wife during a fight in Florida on June 24th.

When cops arrived to the scene, they found the gun -- and according to the police report, Jackson admitted to saying he should shoot his wife ... who he claimed had threatened him with a knife.

But according to new court docs filed in Florida, the Assistant State Attorney says there's just not enough evidence to get a conviction if the case moved forward.

"From the investigation which has been made, it is the opinion of the writer that this case is not suitable for prosecution."