Larger companies like Welsh National Opera (WNO) and National Theatre Wales (NTW) will see budgets fall.
Altogether, 67 organisations will share a funding pot of £27.5m.
ACW chairman Prof Dai Smith said it had been a "challenging" process but a third of organisations - mostly smaller arts groups - will not see any cut.
Opera, theatre and dance companies, as well as educational groups and arts centres, will be finding out about their proposed budgets for 2016/17.
The funding announcement is the final stage of ACW's investment review, the first in five years.
It has now decided how many companies should continue to receive regular core funding, and how much they deserve.
ACW has created a new Arts Portfolio Wales which sees 67 companies receiving funding for their core work, while two organisations receive lottery funding for specific projects and events.
Companies which receive less than £150,000 have been protected from any cuts.
The largest beneficiary of Arts Council funding, WNO, will see its funding fall from £4,539,538 in 2015/16 to £4,380,654 in 2016/17.
But the budgets of two organisations which receive annual grants have been increased. Ballet Cymru's funding rises from £193,842 to £243,842  while Sinfonia Cymru's budget almost doubles from £111,459 during the current financial year to £210,459 from April.
As well as distributing annual grants to fund the core work of Welsh arts companies, called revenue funding, ACW also distributes lottery funding for specific projects.
Prof Smith said the ACW was determined to be "bold, brave and far-reaching".
"In spite of a further £1.5m cut in Welsh government funding, we have been able to sustain a nationwide network of high-performing organisations.
"We have also protected them against the full impact of the cuts."
Of the companies that will receive funding from April, four companies will be members of the portfolio for the first time:
During the investment review a total of 94 companies applied for more than £32m from ACW. As well as four new companies, five others were told they would not continue to be funded from April 2016:

Prison officer Adrian Ismay died days after car bombing in Belfast in March.
DUP MP Gavin Robinson alleged in the Commons that a police email said checks were resulting in "too many complaints" from the suspect's solicitor.
The Police Service of Northern Ireland said they "rigorously enforce all bail conditions set down by the courts".
"If a person is required to wear an electronic tag as part of their bail conditions, there is no reason for police to duplicate this monitoring unless otherwise requested or directed by the investigating officer or senior police officer or the court," a PSNI statement said.
The bail checks refer to Christopher Alphonsos Robinson who has been charged with the murder of Mr Ismay, who trained prison officers at Maghaberry Prison.
Dissident republicans claimed responsibility for the attack.
The accused, from Aspen Park in Dunmurry, west Belfast, was granted bail under strict conditions in May.
The conditions including electronic tagging and an exclusion order for an area of east Belfast.
Speaking during a Westminster debate, the DUP MP said: "I received information at the weekend that PSNI chiefs sent an email to their officers not to conduct bail checks because it was generating far too many complaints from his solicitor and offending his sensitivities."
In response, a PSNI statement said: "Police will continue to rigorously, but impartially, enforce all bail conditions set by the courts and we will not hesitate to arrest those who breach their bail conditions."
The House of Commons debate focused on Libyan-sponsored terrorism.
The MP said Mr Ismay "was blown up by a bomb planted by the new IRA containing Semtex, which is presumed - since there have been no recent purchases - that it is of the same origin and extraction, sourced from the Czech Republic, through Libya to the IRA and disseminated through their splinter organisations."
Arts companies face cuts of up to 3.5% to the public money they will receive from April, the Arts Council of Wales (ACW) has announced.
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Police officers have been asked to stop conducting bail checks on a man accused of murdering a prison officer, the MP for East Belfast has claimed.