The suspect, identified as Randy Nash, was arrested Saturday around 9:13 p.m. in the 1000 block of W. 85th Street in South L.A., according to the Los Angeles Police Department
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Nash, 31, was booked on suspicion of murder and his bail was set at $2 million.
Police say the stabbing occurred around 5:20 p.m. Thursday while the suspect and the victim were aboard the subway train.
The suspect pulled out a knife and "without warning or provocation" stabbed the victim -- identified as Jesse Rodriguez -- in the upper torso, the LAPD said in a statement Friday.
Police said Transit Services Division officers who were at the Pershing Square Station rendered aid to Rodriguez until paramedics arrived.
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Rodriguez later died at a hospital.
Police released a photo of the suspect amid their search.
Security was stepped up in response to the stabbing, with additional LAPD officers patrolling the stations and riding trains this weekend.
City News Service contributed to this report.