Plasma treatment is a method to modify the physicochemical properties of biomaterials, which consequently may affect interactions with cells. Based on the rationale that physical cues on the surface of culture substrates and implants, such as surface roughness, have proven to alter cell behaviour, we used electrospinning to fabricate fibrous three-dimensional scaffolds made of a poly (ethylene oxide terephthalate)/poly (butylene terephthalate) copolymer to mimic the physical microenvironment of extracellular matrix and applied radio-frequency oxygen plasma treatment to create nanoscale roughness. Scanning electron microscopy (SEM) analysis revealed a fibre diameter of 5.49 ± 0.96 µm for as-spun meshes. Atomic force microscopy (AFM) measurements determined an exponential increase of surface roughness with plasma treatment time. An increase in hydrophilicity after plasma treatment was observed, which was associated with higher oxygen content in plasma treated scaffolds compared to untreated ones. A more pronounced adsorption of bovine serum albumin occurred on scaffolds treated with plasma for 15 and 30 min compared to untreated fibres. Clinically relevant human mesenchymal stromal cells (hMSCs) were cultured on untreated, 15 and 30 min treated scaffolds. SEM analysis confirmed cell attachment and a pronounced spindle-like morphology on all scaffolds. No significant differences were observed between different scaffolds regarding the amount of DNA, metabolic activity and alkaline phosphatase (ALP) activity after 7 days of culture. The amount of ALP positive cells increased between 7 and 21 days of culture on both untreated and 30 min treated meshes. In addition, ALP staining of cells on plasma treated meshes appeared more pronounced than on untreated meshes after 21 days of culture. Quantitative polymerase chain reaction showed significant upregulation of bone sialoprotein and osteonectin expression on oxygen plasma treated fibres compared to untreated fibres in basic culture medium after 7 days of culture, while no differences were observed in the expression of other osteogenic markers. At 21 days, no osteocalcin protein could be detected by ELISA at any of the substrates. In conclusion, this study shows that oxygen plasma treatment can successfully be applied to modify the nanoscale surface properties of polymeric electrospun fibre meshes, which in turn may positively affect osteogenic differentiation of hMSCs.