At low frequencies the assessment of the sound reduction index of building elements in the laboratory according to the standard ISO 10140-2:2010 is burdened by a large variation in the measurement results. This is due to the fact that at low frequencies the acoustic field is not sufficiently diffuse. This paper discusses a measurement procedure in which a diffuse field is created in the source room by means of an array of loudspeakers positioned closely to the building insulation element under test. This procedure exploits the acoustic near field of the loudspeaker array. The problems related to the breakdown of the diffuse field assumption of the receiving room are eliminated by measuring the structural response of the building insulation element under test by means of laser Doppler vibrometry and the application of the Rayleigh integral to compute the radiated sound power. The sound reduction index is determined from the ratio of the incident sound power, created by the loudspeaker array, and the radiated sound power. The measurement approach is validated by means of a measurement of the sound reduction index of a single layer glazing. Comparisons are made with an analytical model and with a standardized ISO 10140-2:2010 measurement. Although the method offers clear, strong points in terms of removing room acoustic effects from the measurements in the lower frequency range, a point of concern is the measurement effort.