Yes. MINI is a wholly owned brand of the BMW Group, the German automotive manufacturer headquartered in Munich. BMW acquired the rights to the MINI brand in 1994 when it purchased the Rover Group, which at the time owned the classic Mini nameplate (originally created by the British Motor Corporation in 1959). After BMW sold off most of Rover Group in 2000, it retained the MINI brand and relaunched it in 2001 as a modern reinterpretation of the original small car, built at the Plant Oxford facility in Cowley, England.
Today MINI operates as one of BMW Group's core brands alongside BMW and Rolls-Royce (which BMW also owns, separately from the Volkswagen-owned Bentley). MINI vehicles are engineered using BMW platforms, engines, and technology, and the brand shares BMW's corporate structure, financial reporting, and much of its dealer network infrastructure in many markets, though MINI typically maintains its own distinct dealerships and marketing identity to preserve its youthful, retro-styled brand image.
So while BMW and MINI are marketed as separate brands with different design philosophies — BMW positioned as a premium/luxury performance brand and MINI as a compact, lifestyle-oriented brand — they are legally and financially the same corporate entity: Bayerische Motoren Werke AG (BMW AG). This is similar to how Toyota owns Lexus, or how Volkswagen Group owns Audi, Porsche, and Škoda — distinct brands under one parent company umbrella.
It's worth noting the original Mini (lowercase, one word) from 1959–2000 was a British car made by companies like BMC, British Leyland, and Rover, with no BMW involvement until the mid-1990s acquisition of Rover.