Boris Johnson is under renewed pressure to sack the 48-year-old adviser after it was claimed Mr Cummings travelled to visit his family a second time, despite official guidelines warning against long-distance journeys.
Asked about the first alleged breach of lockdown rules, Mr Shapps told Sky's Sophy Ridge that Mr Cummings was "trying to do the best by the child".
He said: "What they've done is gone to make sure there's a support network around them, both parents were concerned about being ill, so they've gone somewhere which was adjacent to his parents.
"It meant that if they were both ill that the child would be getting support."
He called Mr Cummings' actions "sensible rational steps to make sure that they could look after their child".
Mr Shapps then said the allegations he made a second trip to Durham after returning to London "completely untrue".
“When he came back to London, which was on April 14 I see, he has remained in London since and hasn’t been back to Durham," said the Transport Secretary.
“There are all kinds of things that are being said here that are completely untrue. The basic story is actually pretty straightforward. Husband and wife were ill, they hunker down, they look after their four-year-old and they don’t move until they are better.
“And coming back down to London afterwards, they would have been travelling for essential work which is always allowed as well.”
The Transport Secretary said he was sure Mr Cummings obeyed social distancing rules during the first trip.
He said: “You’ll appreciate I wasn’t with them so I can’t tell you exactly what that journey was like, but what I do know is that Dominic Cummings – I saw a clip yesterday of him asking journalists to be spaced two metres apart, so I know he is a stickler for those rules about what to do to make sure you are following the two-metre rule and the like, so I’m sure that they took all the necessary precautions.”