Yes, they were called the the International Military Tribunal for the Far East (IMTFE) or the Tokyo Trials and the Allied powers convened them in the same spirit as their German counterpart. Like the German tribunals, the Tokyo Trials investigated crimes against peace, crimes against humanity, and war atrocities. Similarly, the Tokyo prosecutors indicted many of the surviving leadership of the old regime, with the notable exception of the Emperor. Many of the problems that plagued the Nuremberg prosecutors also popped up in Tokyo. The tribunals were both subject to scrutiny that they were victor's justice and that the many of the charges were Nulla Poerna Poena Sine Lege (no punishment without prior law). The crimes against peace charge was problematic in particular. In both tribunals, the prosecution argued that there was a general conspiracy to embark on a plan of global domination which involved running roughshod over international law. The problem was there was little evidence of a conspiracy in a legal sense of the word and often these charges were indicting Axis foreign policy, not the individuals that made it. The judges even acceded that in Japan's case that there was no concerted plan to conquer North and South America, thus Japan's imperial ambitions were much more limited in scope than the Third Reich.
The charges of crimes against humanity and war atrocities demonstrate how the Japanese case differed from the German example. Crimes against humanity itself was a new legal concept and only hazily defined, so the prosecution presented tales of atrocity and crimes against the defendants. The problem was that Japanese atrocities were more decentralized and followed a less coherent framework than the Germans. Often prosecutors argued that the defendants enabled Japanese atrocities through inaction rather than direct acts. Further complicating matters was that Japanese leadership was constantly shifting during the war and there was no single organizational analogue to the SS upon which to ascribe the bulk of Japan's wartime guilt. The Tokyo prosecutors had to transform the decentralized nature of Japanese crimes into something coherent; thus the abuse of PoWs in the Philippines was related to the Rape of Nanjing and forced labor in Southeast Asia, which was a hard connection to make. The systematic nature of Nazi genocide was far easier to set as a legal precedent for crimes against humanity.
These differences helped ensure that Nuremberg, not Tokyo, entered into memory as the example of a war crimes trial. The Tokyo Trials were much more ambiguous and thus easily attacked as a form of victor's justice. The absence of Hirohito from the trials was also quite notable as he was one of the few Japanese leaders present throughout the war. Many of the defendants actively colluded to exculpate the Hirohito. This compromised nature has meant that cultural representations of the Tokyo trials differ from those of Germany. Cinematic depictions of the Japanese trials like Blood Oath or Emperor feature their prosecutor protagonists struggling against both Japanese stonewalling and the Occupation officials that want a selective prosecution. In extreme cases like the Japanese film Pride, the trials were a cynical attempt to cement a postwar subordination of Japan to the United States. This is in stark contrast to films about Nuremberg like Judgement at Nuremberg, which hew to the classic norms of a legal thriller (reluctant lawyer, investigation into new evidence, guilty convicts themselves on the stand- edit: I'm talking here about Western and Japanese films about the tribunals, the 2006 Chinese film Tokyo Trial is more traditional legal film, with a heady dose of nationalism thrown in). All of this has ensured that the Tokyo Trials are a relatively forgotten moment in postwar history.
Sources
Dower, John W. Embracing Defeat: Japan in the Wake of World War II. New York: Norton, 2000.
Merritt, Richard L. Democracy Imposed: U.S. Occupation Policy and the German Public, 1945-1949. New Haven: Yale University Press, 1995.