The Monday attack was the third in just over three weeks on Ain al-Assad base in western Iraq, which hosts American troops as well as other personnel from the US-led coalition against the Islamic State jihadist group.
"Make no mistake, the United States will not tolerate attacks on our personnel in the region," Austin told a news conference in Annapolis.
A US defense official said earlier in the day that the attack wounded five American military personnel and two contractors, all of whom are in stable condition.
A Pentagon statement on a call between Austin and his Israeli counterpart Yoav Gallant described the rocket fire as an "Iran-aligned militia attack on US forces" and said the two agreed that it "marked a dangerous escalation."
Such attacks were frequent early in the war between Israel and Hamas Palestinian militants in Gaza, but until recently had largely halted.
The latest rocket fire comes as fears grow of an attack by Iran and its allies on Israel in retaliation for the killing of top Hamas and Hezbollah figures in strikes either blamed on or claimed by Israel.
The killings are among the most serious series of tit-for-tat attacks that have heightened fears of a regional conflagration stemming from the Gaza war.
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