Villa added the 24-year-old, who scored 10 goals in Lazio's run to the quarter-finals of Europe's second-tier competition last term, "will play no further part this season".
The 6-foot-4 inch Kozak, who made his debut for the Czechs in 2012, was signed by Paul Lambert to help take the pressure off Christian Benteke, Villa's only other main target man.
Kozak joined Lazio in 2008 from Czech second division side Slezsky FC Oprava but after a season with the Rome club he went out on loan to Serie B side Brescia. He returned to Lazio where he played 79 times in all competitions, scoring 22 goals.
Aston Villa are in 11th place in the Premier League on 23 points.
(Writing by Ken Ferris; Editing by Greg Stutchbury)
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