Fasini spent his childhood in Odessa and attended the Fine Arts Academy where he was taught by Kiriak Kostandi, an impressionist painter of Greek origin. He became friends with the painter Philippe Hosiasson and the writer Isaac Babel and drew illustrations for Odessa newspapers, including for the Bomba and for the Iablstchko.

In 1922 he travelled to France on a soviet ship and established his residence at rue Daru in Montparnasse. Fasini's painting was situated on the edges of abstraction and surrealism and his work was marked by a desire for new experiences that positioned him uniquely within the School of Paris movement. He acquired a certain celebrity in the period 1920-1925 and the Galerie d'Art Vavin exhibited him for two years alongside Jean Lurçat, Pablo Picasso and Georges Papazoff. Fasini collected tribal art and also showed interest in photography and designing furniture.

During the Occupation, he did not stop painting. His close relations urged him to leave for the Free Zone, but his despair prevented him from doing so. On 16 July 1942 during the Velodrome d¹Hiver roundup, Fasini and his wife were arrested by the French gendarmes and the contents of his atelier were destroyed. They were interned in Drancy and deported on 22 July 1942 on convoy n°9. They were assassinated in Auschwitz.

A bord d'un bateau soviétique, il débarque en France en 1922 et s'installe rue Daru, à Montparnasse. La peinture de Fasini se situe aux marges de l'abstraction et du surréalisme. Son travail est marqué par un désir d'expériences nouvelles qui lui donnent une place originale au sein de l'École de Paris. Il acquiert une certaine notoriété dans les années 1920-1925. Max Berger, propriétaire de la Galerie d'Art Vavin l'expose pendant deux ans avec les peintres Jean Lurçat, Pablo Picasso et Georges Papazoff. Alexandre Fasini collectionne l'Art primitif. Il s'adonne également à la photographie et à la création de mobiliers.

Pendant l'Occupation, il ne cesse de peindre. Ses proches lui recommandent de partir en zone libre, mais son désespoir l’en empèche.Le 16 juillet 1942, lors de la rafle du Vel d’Hiv, Fasini est arrêté avec Rosa sa femme par la police française ; ses oeuvres sont détruites dans son atelier.

Tous deux sont internés à Drancy. Le 22 juillet 1942 déportés convoi n°9
Assassinés à Auschwitz.