The IPL handed Harbhajan an 11-match ban after he admitted slapping fellow India star Santh following the Mumbai Indians' defeat by the Kings XI Punjab.
As the player is centrally-contracted, the BCCI launched a separate inquiry led by commissioner Sudhir Nanavati.
His findings prompted chairman Sharad Pawar to confirm the additional punishment, with a board statement declaring the disciplinary committee had invoked the maximum punishment: 'a ban up to a maximum of five ODIs and/or three Test matches'.
"What I did was wrong. Sree is like my younger brother," said Harbhajan after the IPL's ban was announced on 28 April.
"I regret my actions that have hurt his feelings. I am very apologetic about the whole incident," added the spinner, who also admitted his actions were "grossly wrong".
TV cameras failed to capture the incident but paceman Santh was seen crying afterwards.
The BCCI also warned Santh, saying it would take "appropriate decision" if the fast bowler did not improve his on-field behaviour.
Harbhajan will now miss the June triangular series in Bangladesh against the host nation and Pakistan, along with the Asia Cup later on in the month.
He faced controversy in January over allegations that he called Australia's Andrew Symonds a monkey during the second Test in Sydney.
The off-spinner was eventually cleared of the charge of racial abuse but found guilty of using abusive language.