Depends on what kind of thread. Short answer: 6 + months to years from now.
Cotton threading: 6/months - 1+ year
Polyester: Never seen it dissolve nearing 1 1/2 years
Nylon: Never seen it dissolve nearing 1 1/2 years
Fishing line: Never?
The plant you attached with it will likely cover it up and you more or less forget about it before it dissolves. You'll have better luck waiting until it starts growing in (depending on plant) and attaches, then cut the thread off and remove it manually vs waiting on it if you really want it gone.