Family spokesman Jim McGrath said the 92-year-old was taken to Houston Methodist Hospital on Friday “for observation due to a persistent cough that prevented him from getting proper rest”.
“It was subsequently determined he had a mild case of pneumonia, which was treated and has been resolved,” Mr McGrath added.
“President Bush is in very good spirits and is being held for further observation while he regains his strength.”
Mr Bush spent more than two weeks at the same hospital in January after developing pneumonia – much of that time in the hospital’s intensive care unit.
His wife, former first lady Barbara Bush, 91, was also at the hospital at the same time where she was treated for bronchitis.
Before his election as US president, Mr Bush had served as vice president to Ronald Reagan for eight years.
He is the father of ex president George W Bush and former Florida Governor and Republican presidential candidate Jeb Bush.