Sir Anthony Hart said their inclusion would bring the total number to 22.
He stressed that the inquiry, which has held 157 days of oral hearings, will still complete its work by July 2016.
The HIA was set up in 2013 to investigate child abuse in residential institutions in Northern Ireland over a 73-year period, up to 1995.
These included a range of institutions, run by the church, state and voluntary sector.
Six new institutions to be investigated by HIA
Sir Anthony said that in drawing up the list of six additional institutions, the inquiry had carefully considered information in respect of 54 homes and institutions in relation to which at least one person had made an allegation.
However, he said to hold hearings in respect of each of these could take a further two years and cost at least another Â£8m without significantly adding to the inquiry's understanding of the nature and extent of systemic failings.
The chairman also spoke about the need for financial redress for those who had suffered abuse despite the HIA's investigations still continuing.
'Targeted consultation'
"What we can now say is that from the evidence we have heard so far we will recommend that there should be a scheme to award financial compensation to those children who suffered abuse in children's homes and other institutions in Northern Ireland between 1922 and 1995," he said.
Sir Anthony said the inquiry would be conducting a "targeted consultation" to gather views and suggestions on redress from all the applicants who had contacted either the inquiry or the acknowledgement forum.
The consultation period will run until Friday 8 January 2016 and more details can be found on the HIA website.
Sir Anthony told Banbridge Courthouse on Wednesday that the final decision on redress did not rest with the inquiry.
"Although our terms of reference provide that the inquiry will make recommendations and findings on a number of matters, the final decision as to whether there should be any form of redress, and what form it may take, are matters for the Northern Ireland Executive to decide," he said.
A further six institutions are to be investigated by the Historical Institutional Abuse Inquiry (HIA), its chairman has announced.