City, the world's richest club, were the better side but Salonika produced a determined display to make it 13 wins and 12 draws from 25 home games in Europe since making their debut in the now defunct Cup Winners' Cup against Chelsea in 1970.
Roberto Mancini's team could not get their finishing right and were twice denied by Greece goalkeeper Michalis Sifakis.
Sifakis was first called upon in the 15th minute when David Silva fed Edin Dzeko and the keeper thwarted the Bosnian striker from close range.
Aris went close one minute before half-time when a Darcy Neto free-kick from the edge of the box flashed narrowly past the post with City goalkeeper Joe Hart stranded.
The home team, who knocked out holders Atletico Madrid earlier in the competition, had to resort to long-range efforts from Neto and Juan Carlos Toja in the second half against City's well-organised back-line.
Sifakis produced the save of the night in the 63rd minute when he stretched to palm away a powerful header by Dzeko who also fired wide when well placed.
Aris faded in the later stages but City could not capitalise on their extra pressure and possession.
The second leg at Eastlands is on February 24.
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