The coronavirus disease 2019 (COVID-19) is an unprecedented pandemic that has severely impacted global public health and the economy. Hydroxychloroquine administered orally to COVID-19 patients was ineffective, but its antiviral and anti-inflammatory actions were observed in vitro. The lack of efficacy in vivo could be due to the inefficiency of the oral route in attaining high drug concentration in the lungs. Delivering hydroxychloroquine by inhalation may be a promising alternative for direct targeting with minimal systemic exposure. This paper reports on the characterisation of isotonic, pH-neutral hydroxychloroquine sulphate (HCQS) solutions for nebulisation for COVID-19. They can be prepared, sterilised, and nebulised for testing as an investigational new drug for treating this infection. The 20, 50, and 100 mg/mL HCQS solutions were stable for at least 15 days without refrigeration when stored in darkness. They were atomised from Aerogen Solo Ultra vibrating mesh nebulisers (1 mL of each of the three concentrations and, in addition, 1.5 mL of 100 mg/mL) to form droplets having a median volumetric diameter of 4.3–5.2 µm, with about 50–60% of the aerosol by volume < 5 µm. The aerosol droplet size decreased (from 4.95 to 4.34 µm) with increasing drug concentration (from 20 to 100 mg/mL). As the drug concentration and liquid volume increased, the nebulisation duration increased from 3 to 11 min. The emitted doses ranged from 9.1 to 75.9 mg, depending on the concentration and volume nebulised. The HCQS solutions appear suitable for preclinical and clinical studies for potential COVID-19 treatment.