No, you are not required to have an office to operate an employment agency (EA). However, you must obtain approval from the relevant authorities to use any premises to operate an EA. Examples include the Urban Redevelopment Authority (URA) for private residential premises, and HDB for Housing Board flats.
Nonetheless, MOM reserves the right to step in for exceptional cases (e.g. if sharing premises with an objectionable trade such as a massage parlour or KTV lounge).