Sigit Indrajit was detained yesterday in Jakarta as he got off a boat that had arrived from Sumatra island, national police spokesman Boy Rafli Amar told AFP, adding that he was "the planner of the attack".
The second suspect, identified only as Rohadi, was detained early today at a house on the outskirts of Jakarta where officers found bomb-making materials including fertiliser, Amar said.
"We believe Rohadi played the role of bombmaker," the spokesman said.
Police said they had been planning to attack the embassy in Jakarta the following day.
After the plot was uncovered, police launched a major counter-terror operation focused mainly on the main island of Java, killing eight terror suspects and arresting more than 20 others.
There is growing anger in Muslim-majority Indonesia over religious clashes in largely-Buddhist Myanmar that have left many minority Muslims dead and tens of thousands displaced.