It depends of your definition of Europe but Herodotus talks about the Scythians (Eurasian nomads) gathering in tents to bath in the smoke of heated hemp-seed.
Here's the relevant extract from The History of Herodotus (440 BCE), as translated by George Rawlinson :
After the burial, those engaged in it have to purify themselves, which they do in the following way : First they well soap and wash their heads; then, in order to cleanse their bodies, they act as follows : they make a booth by fixing in the ground three sticks inclined towards one another, and stretching around them woollen felts, which they arrange so as to fit as close as possible: inside the booth a dish is placed upon the ground, into which they put a number of red-hot stones, and then add some hemp-seed.
[...]
The Scythians, as I said, take some of this hemp-seed, and, creeping under the felt coverings, throw it upon the red-hot stones; immediately it smokes, and gives out such a vapour as no Grecian vapour-bath can exceed; the Scyths, delighted, shout for joy, and this vapour serves them instead of a water-bath; for they never by any chance wash their bodies with water. Their women make a mixture of cypress, cedar, and frankincense wood, which they pound into a paste upon a rough piece of stone, adding a little water to it. With this substance, which is of a thick consistency, they plaster their faces all over, and indeed their whole bodies. A sweet odour is thereby imparted to them, and when they take off the plaster on the day following, their skin is clean and glossy.
It's not exactly like smoking a cigarette but I guess it qualifies.
There was a late medieval composer, Solage, who composed a very famous ars subtilior song titled "fumeux fume par fume" which has apparently provoked discussion as to whether people were smoking hashish or opium at this time ( late 14th c.) But the fumeurs mentioned were most likely just a bunch of poets thought to have "smoky" brains.
It is a very strange song, with strange words, and it's easy to assume it was written by somebody on drugs. But I don't know if anyone has actually found evidence for the practice.
Similar post from couple of months ago: http://www.reddit.com/r/AskHistorians/comments/2sodtz/did_people_smoke_other_things_in_europe_before/
Related to the topic: Rodrigo de Jerez was one of the Spanish crewmen who sailed to the Americas on the Santa Maria as part of Christopher Columbus's first voyage across the Atlantic Ocean in 1492. He is credited with being the first European smoker. I'm mentioning this because his story is quite interesting and hilarious. More here under European discovery.
I'm wondering how much truth there is to the Rodrigo story?
As an offshoot question, what about opium? Wikipedia claims medicinal use of the opium poppy predates written history. Can it be smoked, and is there any evidence of that in antiquity?