Augsberg Airlines, which flies on a number of internal German routes, is test-marketing the cigarettes for the Reynolds Tobacco company, manufacturers of the cigarettes which glow when lit.
It does not give off smoke or ash, but the glowing tip of the cigarette consists of a type of coal which heats the air gently. This hot air releases the flavour - but after six to eight minutes, the cigarette loses the taste and must be put out.
The cigarettes contain only 0.2mg of nicotine and 3mg of tar, compared to, say, Benson & Hedges, which have 0.9mg of nicotine and 7mg of tar. The cigarettes come in two flavours, menthol and original.
Reynolds say that the cigarettes have been tested independently by the government in Germany, which has found no problems with them.
The cigarette is also scheduled to be tested in the United States, Sweden, and if they prove successful will be tried in the UK.
The cigarettes are being described by Augsberg Airlines as a "smokeless, odourless cigarette" and are handed out to customers for free. The company says its air hostesses have to be "briefed on how to light the cigarette before take-off" because they contain "glowing ash like coal which give off hot air".
An airline spokeswoman told the Independent that it handed out questionnaires to the passengers and "the cigarettes have had a positive response with non-smokers, who have not been affected by them in any way". She said that a passenger sitting next to a smoker may not even realise the person was smoking.
However, she said that some smokers had complained that they were "not enamoured with the taste".
She added: "We are not advocating smoking in any way. The airline is not advertising the cigarettes at all, but Reynolds are promoting them."
The anti-smoking group, ASH, was critical of the experiment. A spokeswoman said: "We see these cigarettes as undermining the government's campaign against smoking. The cigarettes may actually contain more carbon monoxide than normal cigarettes, so may prove to be more harmful than others."Reuse content