Mr Wood tipped off parents on the Clopton Road Estate, Garrets Green, when known paedophile George Taylor moved into a flat last autumn.
Taylor, 58, moved in with his 83-year-old widowed mother after release from prison for sexually assaulting a young girl. He was removed by police for his own safety three weeks later when residents protested against his presence, but returned a day later.
He spent two further days on the estate under police protection before being moved by the council to a secret address in another part of the city with his mother.
Petitions from council tenants backing Mr Wood's actions have been handed in and residents have called for him to be reinstated.
Liberal Democrat councillor John Hemming is also supporting Mr Wood.
He said: 'Mr Taylor should not have been housed on the estate and I don't believe Mr Wood should be in danger of losing his job as a result of what he did.
'He believed he was helping to ensure the safety of children and other tenants on that estate.'
A West Midlands Police spokesman said: 'We can confirm that Mr Taylor was recently released after serving a prison sentence for the indecent assault of a young girl.'
Birmingham spokeswoman Ann Fleming said the authority had no knowledge of Taylor's background when he moved in with his mother: 'We are not told of the previous convictions of tenants under any circumstances.'