Grinevetsky was born on the 2nd of June (14th old style) 1871 in Kiev to the family of a railway employee, State Counsellor Ignatii Feliksovich Grinevetsky, who belonged to an old noble family, and his wife Ekaterina Vasilievna, the daughter of Admiral Vasily Zavoyko, who had organised the successful defence of Petropavlovsk, Kamchatka from the Anglo-French fleet during the Crimean War. However his mother died when he was six, and the family moved to Kremenchug, where his father had been reposted. Then the family moved on to Kazan where attended Kazan Real School. As a child he developed an interest in machinery, building a working roller mill on his grandmother's estate.