The practice is to put up a mezuza without a blessing. The simple summary (from aish) is
Some of the earlier authorities did not consider an office a true
place of residence since we do not truly live there. Later
authorities, however, disagree since people typically do eat and
sometimes nap or sleep in their offices. As a result, today the
practice is to put a mezuzah up in an office, but without a blessing.
dinonline brings the halachic reasoning
The Shulchan Aruch (YD 286:11) rules that a store in the marketplace
does not require a mezuzah. The Levush (YD 286:11) and Shach (ibid 21)
explain this is because a store is a temporary dwelling, and the Torah
requires a mezuzah only on permanent residences. The Shulchan Aruch
compares a store to a succah on Succos and a ship’s cabin in their
(non)-mezuzah obligation.
This halacha puzzles contemporary poskim since we are required to
affix a mezuzah on storage room doorposts, and if comparing their
doorpost’s volume of traffic, stores rate much higher. Besides, a
store is also used to “store” merchandise both when open, and closed.
Why, therefore, should a store require a mezuzah less than a storage
space?
- The Taz maintains (YD 286:10) that a store is only used during the day and not at night, and in order for a space to be considered
inhabited it has to be used for its designated purpose both day and
night. Although it also serves to store merchandise, the space is not
intended for storage. Rather, its main purpose is commercial, and
storage is only a secondary use.
- The Yad Haketana (Mezuzah 2:21, quoted in Pischei Teshuva footnote 10) disagrees with the Taz’s explanation. In his opinion, the Shulchan
Aruch refers here to a storefront from which merchandise is removed
every night, or a stall in the marketplace that is used only on market
days. This is the kind of store for which a mezuza not required, but
other stores do require a mezuzah. (This opinion is also mentioned in
the Ben Ish Chai [Rav Pe’alim II YD 36:3). [...]
- Rav Moshe Feinstein (Igros Moshe YD I, 178) rules that if a business is not active every day it is certainly exempted from
mezuzah. Apparently, he follows the Taz’s opinion that exempts every
store and business from affixing a mezuzah despite serving as a
storage for merchandise or business tools. He does, nevertheless, take
in account the Yad Haketana’s opinion, and therefore requires a
mezuzah affixed on a business doorpost, albeit without a bracha.
- Rav Elyashiv, though (Shvus Yitzchak chapter 2:2) requires a mezuzah affixed on a store with a bracha.
Many poskim rule differently in this matter, depending upon various factors such as if there is a coffee room or not, and how a business
is used. Every case requires individual consideration and ruling, and
one business cannot be compared to another.
For further halachic references see also here.