Aims: IKT 16 is an X-ray and radio-faint supernova remnant (SNR) in the Small Magellanic Cloud (SMC). A previous X-ray study of this SNR found a hard X-ray source near its centre. Using all available archival and proprietary XMM-Newton data, alongside new multi-frequency radio-continuum surveys and optical observations at H-alpha and forbidden [SII] and [OIII] lines, we aim to constrain the properties of the SNR and discover the nature of the hard source within. Methods: We combine XMM-Newton datasets to produce the highest quality X-ray image of IKT 16 to date. We use this, in combination with radio and optical images, to conduct a multi-wavelength morphological analysis of the remnant. We extract separate spectra from the SNR and the bright source near its centre, and conduct spectral fitting of both regions. Results: We find IKT 16 to have a radius of 37+-3 pc, with the bright source located 8+-2 pc from the centre. This is the largest known SNR in the SMC. The large size of the remnant suggests it is likely in the Sedov-adiabatic phase of evolution. Using a Sedov model to fit the SNR spectrum, we find an electron temperature kT of 1.03+-0.12 keV and an age of 14700 yr. The absorption found requires the remnant to be located deep within the SMC. The bright source is fit with a power law with index 1.58+-0.07, and is associated with diffuse radio emission extending towards the centre of the SNR. We argue that this source is likely to be the neutron star remnant of the supernova explosion, and infer its transverse kick velocity to be 580+-100 km/s. The X-ray and radio properties of this source strongly favour a pulsar wind nebula (PWN) origin.