In a ruling with wide implications, top judges ruled DNA testing is a "serious step" that would "psychologically invade" the father's right to a personal life.
The father launched child abduction proceedings against the mother after she left their native Latvia with their girl this year, travelled to the UK and went to ground in Glasgow.
He was due to pick up his daughter from Glasgow Airport in May but, when he arrived with air tickets, mother and daughter were nowhere to be found and it took him weeks to find them.
The mother then said he was not the girl's biological father.
The man asked a family court to order the girl's return to Latvia but, in July, a judge in London told the girl, and both parents, to undergo DNA tests.
Upholding the father's appeal, Lord Justice Longmore, said the Latvian courts had proceeded on the assumption his paternity was not in doubt.
Noting that DNA testing is "a serious step for any court to take", the judge added: "It may not be a physical invasion of privacy since samples can be obtained without any substantial physical bodily interference, but it is on any view a psychological invasion of a litigant's rights to a personal life."
The judge, sitting with Lord Justice Underhill and Lady Justice Macur, said: "It seems to me, therefore, that DNA testing, if it is to be done at all, should only be done as a last resort."