The jet flew from Sanaa, which Houthi rebels overtook in January, to the palace in the port city of Aden, where the jet conducted the strikes Thursday afternoon, a senior air force official said on condition of anonymity.
Deposed President Abdu Rabu Mansour Hadi was at the Aden palace compound when the first missile struck the grounds, but he then fled safely, a Hadi aide said, also on condition of anonymity.
A second missile struck near the compound, but, like the first, injured no one, two officials in Aden said.
Another Houthi-commanded air force jet fired a missile in downtown Aden about a half-hour later, again injuring no one, Aden Gov. AbdulAziz Hobtour said. It wasn't immediately clear what the missile struck, or what the intended target was.
The airstrikes came on the same day opposing Yemeni military forces -- those commanded by Houthis, and those led by officers loyal to Hadi -- battled in Aden, leaving at least 13 people dead and 21 others injured, Hobtour said.
The Houthis, a minority rebel group that holds sway in the nation's north but has less influence elsewhere, took control over military forces stationed near Sanaa, including the air force, as it overtook the government there in January.
Hadi initially was put under house arrest in Sanaa,
but he escaped last month, fleeing to Aden and declaring himself to still be president. Some military forces still are loyal to Hadi, including troops from his native province in the south.
On Thursday, clashes erupted in Aden when a special forces commander loyal to the Houthis, Abdul Hafez Al Saqqaf, ordered hundreds of his troops to create checkpoints at all roads leading to Aden's airport.
The clashes were reported to be taking place on four different fronts in the airport and a surrounding military base. Passengers were stranded at the airport, with flights canceled throughout the day.
Al Saqqaf's forces gave up much of their ground in Aden after pro-Hadi forces struck them with heavy artillery and tanks, a pro-Hadi military commander said on condition of anonymity.
Some of the wounded in Thursday's fighting were in critical condition, officials said, suggesting the death toll could rise.
The Houthis entered Sanaa in September, demanding a greater share of political power.
They took control over a period of months, seizing the presidential palace
in January. The unrest has plunged Yemen deeper into chaos.
Hadi had issued a presidential decree replacing Al Saqqaf two weeks ago, but the decree was not implemented.