He said earlier this week that attacks on Saudi airports are an effective strategy to combat the blockade of the airport in Yemen's capital, Sanaa, which the Houthis overran in 2014.
The missile reportedly caused some damage to the airport's arrivals lounge and flights were disrupted for several hours before returning to normal.
The list of injured passengers includes three Saudi, Yemeni and Indian women and two Saudi children.
The rebels said they had launched a missile at Abha airport but insisted they had the right to defend themselves in the face of years of Saudi-led bombing, and an air and sea blockade.
In May, the Shiite Huthi rebels also carried out twin drone attacks on the kingdom's strategic east-west oil pipeline, forcing a two-day closure of the main diversionary route for Saudi exports avoiding the Gulf.
"Evidence indicates Iran's Revolutionary Guards supplied the Houthis with the weapon that targeted Abha airport", Saudi-owned Al Arabiya TV quoted the coalition as saying.
Almalki stressed that in the face of the Houthi militia's terrorist attacks as well as its immoral violations, the Command of Joint Forces of the Coalition would take urgent and timely measures to deter such attacks and ensure the protection of civilians and civilian objects.
A Houthi military spokesman Tuesday threatened that the group would target every airport in Saudi Arabia and that the coming days would reveal "big surprises".
Indian Express noted that Japan is traditionally a major customer for Iranian oil and has pursued mostly commercial interests in the Middle East since World War II, giving it a greater presumption of neutrality than most other close USA allies.
Wednesday's missile strike hit the civil airport in the mountain resort of Abha, which is a popular summer getaway for Saudis seeking escape from the searing heat of Riyadh or Jeddah.
Saudi officials said that attack was ordered by Iran, but didn't provide evidence to back their claims. In March 2018 an Egyptian was killed in Riyadh by missile shrapnel.
Al-Masirah said it was the second time the Houthis had fired a cruise missile.
The Houthi group last month stepped up its attacks following a lull a year ago ahead of United Nations -led peace efforts.
The incidents sparked fears of a Gulf war breaking out "by accident" with the US and Iranian militaries on high alert amid high tensions between Washington and Tehran. The coalition has responded by carrying out air strikes on Houthi-held Sanaa.