FIFA says the clubs were punished for "breaching their obligation to keep data contained within the FIFA Transfer Matching System strictly confidential."
They are the first such social media offences sanctioned by FIFA.
Persebaya Surabaya and Persires Bali Devata were each fined 25,000 Swiss francs ($25,800) for publishing confidential data. PSIS Semarang was fined 15,000 Swiss francs ($15,500) for "republishing those tweets and publishing a confidential letter sent to them by FIFA TMS."
FIFA's online monitoring was designed to clean up international transfer finances, and was made mandatory in 2010 for all cross-border deals.
Both trading clubs must input the same financial information before FIFA approves a deal.