Ms Irani also took part in "Shala Praveshotsav" (school enrolment festival), an annual event organised by the state government. Ms Patel inaugurated the three-day fest yesterday.
"Union HRD Minister Smriti Irani came today to take part in Shala Praveshotsav - an auspicious event for primary education in Gujarat," an official release said in Gandhinagar.
Ms Irani met Patel in the morning and discussed the success of the state government's different education programmes for girls, it said.
"Met Smt AnandiBen Patel, Hon CM Gujarat at Gandhinagar today," Ms Irani tweeted while sharing her picture with the first woman Chief Minister of Gujarat.
"Sharing photographs of Shala Praveshotsav and Kanya Kelavani Mahotsav at Primary School, Kudasan, Gandhinagar," she tweeted while sharing some of her photos with school kids.
Ms Irani, who visited Gujarat for the first time after becoming the Union Minister last month, later inaugurated a school in Kudasan.
The 'Praveshotsav' initiative was started 12-years ago by then Chief Minister Narendra Modi and is celebrated every year across the state to increase school enrolment in government primary schools.