The features developed in less than 10 hours, covering an area of up to 1000 x 500 km, and remained visible for around 10 days, changing their structure from day to day.
The plumes were seen rising to altitudes of over 250 km above the same region of Mars on both occasions.
"At about 250 km, the division between the atmosphere and outer space is very thin, so the reported plumes are extremely unexpected," said Agustin Sanchez-Lavega of the Universidad del Pais Vasco in Spain, lead author of the paper published in the journal Nature.
None of the spacecraft orbiting Mars saw the features because of their viewing geometries and illumination conditions at the time, researchers said.
However, checking archived Hubble Space Telescope images taken between 1995 and 1999 and of databases of amateur images spanning 2001 to 2014 revealed occasional clouds at the limb of Mars, albeit usually only up to 100 km in altitude.
But one set of Hubble images from May 17, 1997 revealed an abnormally high plume, similar to that spotted by the amateur astronomers in 2012.
Scientists are now working on determining the nature and cause of the plumes by using the Hubble data in combination with the images taken by amateurs.