Nikita Mazepin and father, Dmitry, have both been added to the European Union's sanctions list.
They are two of 14 Russian business people to be sanctioned due to links to Russia's government.
The move comes as pressure continues to grow on the Kremlin in the wake of the ongoing invasion of Ukraine that has seen over two million refugees flee the Eastern European country.
Mazepin Jr was dropped by Haas as the team responded to the crisis, as well as severing ties with sponsor Uralkali, the potash fertiliser producer owned by Mazepin Sr.
Both names appeared on a document published in the official journal of the European Union, listing the 14 people added to the ever-growing sanctions list.
The reasons behind Mazepin Jr's place on the list stated: "Nikita Mazepin is the son of Dmitry Arkadievich Mazepin, General Director of JSC UCC
"As Uralchem sponsors Haas F1 Team, Dmitry Mazepin is the major sponsor of his son’s activities at Haas F1 Team.
"He is a natural person associated with a leading businessperson (his father) involved in economic sectors providing a substantial source of revenue to the Government of the Russian Federation, which is responsible for the annexation of Crimea and the destabilisation of Ukraine."