Poly(ethylene 2,5-furandicarboxylate) (PEF) is an attractive bio-based alternative to petroleum-based polymers. In this work, novel PEF-based nonwovens were obtained by the solution electrospinning, using as solvents: trifluoroacetic acid, its mixtures with dichloromethane and dichloroethane, and also 1,1,1,3,3,3-hexafluoro-2-propanol. The effect of the solvent type and PEF concentration on the fiber thickness and the properties of nonwovens was studied. The average thickness of nonwoven fibers ranged from 180 nm to 2.3 μm. The fibers were amorphous with the glass transition temperature of 85–87 °C. The nonwovens were strongly hydrophobic, with water contact angles of 144–146° although they exhibited the rose petal effect. The mechanical properties of the materials were influenced by their porosity and fiber thickness. The nonwoven electrospun from 20 wt% PEF solution in trifluoroacetic acid, with an average fiber diameter of 2.13 μm and a porosity of 74%, exhibited the highest tensile strength and elongation at break, 10.8 MPa and 190%, respectively.