The fighting on Saturday was the first between the two sides and many Somalis fear it may signal a slide to war in the Horn of Africa country.
Government militia seized and set on fire two "technicals" - heavily armed pickup trucks that are Somalia's version of tanks - in fighting in the remote Qoryooley district, an Islamist source said.
There was no word on any casualties in the clash.
Also on Saturday, Ethiopia said it would "crush" the Somali Islamists, a day after it threatened a holy war against Addis Ababa, which it accused of sending troops to protect Somalia's weak interim government.
The warning came as witnesses reported an incursion of Ethiopian troops into a second Somali town close to Baidoa, the seat of the country's UN-backed but toothless government, ostensibly to protect it from any advance by the Islamists.
Residents in the town of Wajid, some 100km south of the Somali-Ethiopian border, said about 250 heavily-armed Ethiopian soldiers arrived early in the day.
But a district official in Wajid denied the presence of the troops.
Ethiopia and the Somali government have denied any incursion by Addis Ababa's troops.
A Somali government spokesman said: "This is absolute propaganda from the Islamists. There are no Ethiopian troops in Baidoa. Anybody with the evidence should come forward."
Addis Ababa vowed to "crush" the Islamic militia if they dared cross into its territory.
"Ethiopia has made it clear on several occasions that there is a border line they don't have to cross, if they do they will be crushed," a senior government official said on condition of anonymity.
Call to arms
On Friday, the leader of Somalia's Islamist movement had urged his countrymen to wage a "holy war" against Ethiopia.
The call from Sheik Hassan Dahir Aweys, head of the consultative Union of Islamic Courts' Shura, came a day after Ethiopian troops moved into Baidoa.
Aweys said Ethiopia deployed troops "to protect a [Somali] government which they set up to advance their interests".
Sheikh Sharif: Those who side with
Ethiopia will be deemed traitors
He said Abdullahi Yusuf, the Somali president and his longtime rival, has "been a servant of Ethiopia for a long time".
Residents of Baidoa reported the arrival of nine large Ethiopian military vehicles carrying supplies, but no troops, early on Friday.
Sheikh Sharif Ahmed, chairman of the executive committee of the Supreme Islamic Council of Somalia, said: "Somalia is under attack and Somalis must defend their country.
"Anybody who sides with Ethiopia will be considered a traitor."
He was speaking from Mogadishu, the Somali capital, which the Islamists seized from a US-backed alliance of militia commanders last month.
"We are urging Ethiopia to immediately and without delay withdraw its troops and stop interfering in Somali affairs," Sheikh Sharif said.
A convoy of more than 100 trucks with several hundred Ethiopian soldiers rolled into Baidoa and surrounding areas on Thursday, after Islamist militia advanced on a nearby town.
The Islamists pulled back on Thursday, but the Somali prime minister, Ali Mohamed Gedi, accused them of plotting to attack his government in violation of a truce and mutual recognition deal.