After the 1994–95 European season, Sabonis and Portland contacted one another about a move to the NBA. Before signing Sabonis, Portland's then-general manager, Bob Whitsitt, asked the Blazers team physician to look at Sabonis' X-rays. Illustrating the impact of Sabonis' numerous injuries, Whitsitt recalled in a 2011 interview, that when the doctor reported the results, "He said that Arvydas could qualify for a handicapped parking spot, based on the X-ray alone." Nevertheless, the Blazers signed Sabonis. He had a successful rookie campaign, averaging 14.5 points, on 55% shooting, and 8.1 rebounds per game, while playing less than 24 minutes per game. Sabonis was selected to the All-Rookie First Team, and was runner-up in both Rookie of the Year and Sixth Man of the Year voting. His postseason averages went up to 23.6 points and 10.2 rebounds per game. In the first playoff series of his NBA career, Portland lost to Utah, in five games. Sabonis averaged 16.0 points, 10.0 rebounds, and 3.0 assists per game, in 1997–98, all career-highs.
He won the Euroscar twice, while playing with the Blazers. He also became a fan favorite, and had a warm welcome back when he visited Portland in 2011, en route to being enshrined into the Naismith Hall of Fame.
The 1985–1988 stretch of a heavy playing schedule, and lack of rest, took a significant toll on Sabonis' future health and durability. Various leg injuries were not given much time to heal, due to the Cold War climate that surrounded international competition, as well as the intense rivalry of the Žalgiris Kaunas versus CSKA Moscow games in the USSR Premier League. In a 2011 interview, Sabonis expressed an opinion, that overuse by the coaches of the Soviet national program, was a major contributing factor to his first Achilles' tendon injury, back in 1986. Another key moment for his future health, took place in 1988, when Sabonis had a surgical Achilles procedure performed in Portland, but was rushed back on the floor with the USSR Olympic team, before a full recovery. The decision to include a limping Sabonis, on the USSR roster for the 1988 Olympic Games, was protested at the time by the Portland medical staff, and was later heavily criticized. While the Soviets cleared him to play professionally in 1989, when his Soviet national teammate, Šarūnas Marčiulionis, went to North America, Sabonis postponed his travel, over feeling that he was not physically ready for the NBA. Eventually, Sabonis would develop chronic knee, ankle and groin issues, that substantially limited his mobility and explosiveness, by the mid-1990s.
In September 2011, Sabonis suffered a heart attack, while playing basketball in Lithuania. Doctors said that the heart attack was not life-threatening.