No it doesn’t. Plutonium is an alpha emitter - you don’t need any shielding at all. What you DO need is a fair amount of conventional explosives arranged with rather precise geometry to implode your 5-10 kg plutonium core into a supercritical mass, and a whole lot of precision initiators and a neutron generator to light them off, respectively. Which in an old “Fat Man” type device did come to about a thousand pounds but today we can do rather better and you can indeed fit a fission bomb in your backpack.
If you want something else for a nasty plot device, google “gamma kolos” - lots to play with there!