Mohammed Miah, 37, of Poplar, was told he must serve at least 18 years for killing baby Rifat.
A post-mortem examination of Rifat's body found 38 rib fractures, eight leg fractures and a broken spine.
His wife Rebeka Nazmin, 32, was cleared of murder but found guilty of allowing the death of her baby and causing him suffering.
Nazmin, who was said to be in the "thrall" of her husband, was sentenced to six years in prison.
The trial heard how Rifat was also hit with the cord of a mobile phone charger and burned on a radiator.
Both Miah and Nazmin had tried to blame a young autistic child in the house, who had behavioural problems in the past, for the murder.
The jury heard Rifat was subjected to "systematic" abuse while in the care of his parents, culminating in fatal brain injuries in July last year.
Sentencing, Mr Justice Spencer told Miah only he could know why he abused his son - whether it was an "angry response" to being laid up all day with a bad back or "deliberate cruelty".
He told Nazmin: "But for your failure to protect Rifat from his father he might well still be alive."
A father who tried to blame an autistic boy for killing his 13-week-old son has been jailed for murder.