Findings were due to be published in March, more than six years after the Scottish Government pledged to hold an investigation.
The wife of Lord Penrose, who is chairing the inquiry, died towards the end of last year, and this is among the reasons for the postponement.
Statutory processes are also said to be taking longer than anticipated, as well as final work on statistics.
A statement said: "Lord Penrose appreciates and deeply regrets that the delay will cause dismay to many with an interest in the inquiry's outcome.
"Despite his difficult personal circumstances, Lord Penrose remains committed to publishing his final report as early as possible and the report is now in its concluding stage."
The statement said that a further update would be provided at the end of February.
The Penrose Inquiry was set up in 2008 to investigate the scandal which saw hundreds of patients infected with hepatitis C and HIV through contaminated blood used in NHS hospitals in the 1970s and 1980s.
The inquiry came to an end in March 2012 and figures published two months later showed the cost of proceedings was £9 million at that stage.
A separate major Scottish public inquiry into deaths from Clostridium difficile at the Vale of Leven Hospital in Dunbartonshire has also suffered multiple delays and is expected to be published this March.
Opposition politicians have raised concern about the delays affecting both inquiries.