Cleveland Guardians pitcher Luis Ortiz made his first court appearance in his pitch rigging case on Monday ... with the 26-year-old being granted his release with several conditions.

Ortiz appeared before a judge in Boston ... where he walked out of the courthouse after posting a $500,000 bond, $50K being secured. He was ordered to surrender his passport ... and his travel has been restricted to the Northeast. TMZSports.com

Cameras were rolling as Luis left in a tracksuit, but he kept his lips sealed as he got into the waiting vehicle.

The four-year MLB veteran was arrested Sunday at Logan Airport in Boston ... and we obtained a photo not long after Ortiz was met by cops.

Prosecutors unsealed the indictments on Sunday, alleging that Ortiz and his teammate -- Emmanuel Clase -

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