Uukkivi's diploma production roles include Snug in William Shakespeare's A Midsummer Night's Dream and Man in Purple in Mati Unt's Emperor Nero's Private Life.

[1] Among his graduating classmates were Merle Palmiste, Kristel Leesmend, Andres Raag, Kaili Närep, Jaanus Rohumaa, Üllar Saaremäe, Dan Põldroos, Sten Zupping, Tiina Mälberg and Garmen Tabor.

[2] In 1991, Uukkivi made his stage debut at Tallinn's Estonian Drama Theatre in a production of Luigi Pirandello's Six Characters in Search of an Author.

Uukkivi's stage debut as an actor formally engaged at the theatre was as Manuel in a production of Neil Simon's The Gingerbread Lady.

During his long career at the Estonian Drama Theatre, he has appeared in over seventy roles in stage productions of works by such varied international authors and playwrights as: Yasmina Reza, Eugene O'Neill, Michel de Ghelderode, Sławomir Mrożek, Tankred Dorst, Henrik Ibsen, Frank Wedekind, Peter Shaffer, Tony Kushner, Charles Dickens, J.

B. Priestley, Ray Cooney, Ayn Rand, Arthur Miller, Evgeny Schwartz, Brian Friel, Pedro Calderón de la Barca, Victor Pelevin, Roald Dahl, Ivan Turgenev, Juan Rulfo, Lyle Kessler, Tom Stoppard, and Anton Chekhov, among others.

Among his more memorable performances in roles by Estonian playwrights and authors include those of: Uku Uusberg, Martin Algus, Vaino Vahing, Andrus Kivirähk, Oskar Luts, Madis Kõiv, and Eduard Vilde.

Täna öösel me ei maga (English release title: Set Point) is notable for Estonian model Carmen Kass appearing in a starring role.

[17][18] In 2012, Uukkivi appeared as a tough crook in the Andres Kõpper and Arun Tamm-directed dark comedy-crime film Vasaku jala reede.

[28][29] In the early 1980s, Ivo Uukkivi (nicknamed Munk) was the vocalist of a short-lived Tallinn-based punk rock band called Kopli Otell.