In separate phone calls late Sunday, President Raisi urged the two officials to fully utilize available resources to provide proper care to those injured in the attack.
The Iranian president, who is also the chairman of the Supreme National Security Council (SNSC), ordered Vahidi to closely and rapidly investigate the security dimensions of the incident and report the result.
He extended his condolences to the bereaved families of the victims.
At least one person was killed and eight more were injured in the attack on Shah Cheragh holy shrine in the southern Iranian city of Shiraz, according to top government officials in Fars province, where Shiraz is located.
Early reports indicated that the attacker had opened fire at people after being confronted by security guards at the gates of the shrine.
Fars Deputy Governor Esmail Ghezel Sofla described the attacker as a Takfiri element and said the person had been arrested and was being interrogated by judicial authorities.
Shah Cheragh was subject of a major terrorist attack in October last year that led to deaths of 13 people.