The incident took place at the Occidental Petroleum Corp in the Shabwa province in the south of the country, some 500km south of Sana.
Ali al-Maqqdishi, the governor of the province, identified the guard as Jamel Mohammed el-Raaie, and said he was mentally disturbed.
Yemen is an independent oil producer and pumps about 450,000 barrels a day.
The country signed a production-sharing agreement with Occidental Petroleum in March for a block in Shabwa.
A Yemeni security official, speaking on condition of anonymity because he was not allowed to give statements to media, said the wounded were transferred to a hospital in Sana for treatment.
The official said that the victims were all coming off an aircraft that was landing at the oil company's airstrip in Shabwa when the guard randomly opened fire at them. The victims' names were not known.
The US embassy has cancelled all travel to the bordering Shabwa and Mariba governates "for the near future" and recommended that Americans avoid the areas, according to the message on its website.
No further details were immediately available.
Occidental Petroleum Corp is a California-based international company with oil and gas operations in three core areas - the US, Latin America and the Middle East, including Yemen.
It has extensive operations in the Middle East, producing oil in the UAE, Qatar, Oman, Yemen and Libya.