The idea of high buildings can be traced to many centuries

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The idea of high buildings can be traced to many centuries ago when monarchs built, fortresses on elevated hill-tops, from where they could keep the surrounding areas under surveillance. Such a building was also useful for the deference of the city. Ancient fortresses overlooking a vast expanse of land are historical examples that are found in abundance in most countries.
High Buildings in Pre-Islamic Period:

One of the most glamorous citadels, still extand in the south-west of Iran (Province of Khouzestan), is Chogha Zanbil Ziggurat which was built by the Elamite Empire in 1250 BCE. This temple was built in the shape of a stepped pyramid, originally having five stories. Remain of the building has a high of 25 meters though it is believed that the building was initially 50 meters high.
During the Median Empire, residential houses were often built in the low lands whereas the uplands were designated for the royal palaces. The most notable among high buildings remaining from that period are the ones situated on hill-tops in an ancient town called Noushijan.
Other is the tombs of the famous persons built on top of Davood Akhtar Mountains.

The era of the Achaemenids gave rise to newer forms of high buildings such as Pasargade, Persepolis, Zoroasstrian temples and some kinds of minarets that were erected for the purpose of making public announcements. The Parthians revived the architectural glamour of the latter dynasty. Roadside minarets, Fire altars, Zahak citadel, Anahita temple are among the major buildings remaining from the Parthian period.

Among the Sassanid high buildings Taqe-Kasra stands out as most notable. In addition, there were many fire-temples in the provinces like Khorasan, Isfahan and Azarbaijan. Fortresses constructed on hill-tops are among other examples of the Sassanid buildings.

Islamic era:

Basically, a minaret is a slender tower built at the side of a mosque from which the call to prayer is given for Muslims. The tall structures built on roadsides or near caravansaries, schools, or other gathering places were originally watch-towers that also provided lighting for the surrounding areas.
The construction of minaret in its present form was first introduced during the reign of the Ommayad caliphs. The earliest minaret is thought to have been built in late 7th century CE.

In Iran, Minarets first appeared in the form of simple guiding poles near the mosques before being developed into elaborate structures flanking mosques and the entrance of monumental buildings. The minaret of Shoushtar Jame mosque built in the early 8th century CE is among the first minarets erected in Iran following the advent of Islam. In the 8th century CE minarets were made with mud-bricks. It was not until the 9th century CE that the first brick-made minaret was built.

In addition to the minarets of Shoush, Damghan and Qom, we may make a mention of Isfahan's Jourjir mosque minaret which was built in the late 10th century CE. Presumably, the oldest brick-work minaret is the one made 26 Km from the city of Mashhad during the rule of Soltan Mahmoud Ghaznavi (998–1030 CE).
The Seljuq period is particularly noteworthy in the development of architectural arts in Iran, especially with respect to minarets. The minarets also rose at the sides of government building; in the city of Kashan may be cited as outstanding examples. Red mosque in Saveh (built in 1087 CE) is regarded as a Seljuq monumental building.

In the eras of the Moguls, Timurids and Safavids, also mosques and shrines with towering minarets in large numbers were built. There is a famous minaret in Mashhad's Goharshad mosque which belongs to the Timurid period.The Safavids period is known as the golden age of the Iranian architectural arts. Minarets were decorated with colored faience and patterned tiles. The Imam mosque, Chahar Bagh building and Shah Mosque in Isfahan display the most elegant minarets of the era.

With the fall of the Safavids and the emergence of the Qajar dynasty Iranian architecture witnessed a decline and the number of minarets built or repaired in that period is insignificant.