Flower was born in Cape Town, South Africa, and starting from his high school days at Oriel Boys' High School and Vainona High School played most of his career alongside his younger brother Grant Flower. He is considered to be one of the best wicket-keeper batsmen, alongside players such as Australian Adam Gilchrist. Flower made his international debut in a One Day International against Sri Lanka at New Plymouth, New Zealand, in the 1992 Cricket World Cup. A good player of spin, he made 550 runs in a Test series against India in 2000/01. This tally came in just four innings and he was only dismissed twice. He is one of the few players to score a century on ODI debut.

Towards the end of his career, Flower achieved international recognition when he and teammate Henry Olonga wore black armbands during the 2003 Cricket World Cup match against Namibia to protest against Robert Mugabe's policies. He and Olonga released a statement on 10 February, stating in part:

In all the circumstances, we have decided that we will each wear a black armband for the duration of the World Cup. In doing so we are mourning the death of democracy in our beloved Zimbabwe. In doing so we are making a silent plea to those responsible to stop the abuse of human rights in Zimbabwe. In doing so, we pray that our small action may restore sanity and dignity to our Nation.

This act led to pressure from Zimbabwe's government and Flower's retirement from Zimbabwean cricket. He later played an English county cricket season for Essex and an Australian domestic season for South Australia.

Flower played 63 Test matches for Zimbabwe, scoring 4,794 runs at an average of 51.54 and taking 151 catches and 9 stumpings, and 213 One Day Internationals, scoring 6,786 runs at an average of 35.34 and taking 141 catches and 32 stumpings. He holds the Zimbabwean records for the most Test career runs, the highest Test batting average, and most ODI career runs. He is the only Zimbabwean in the ICC's Top 100 All-time Test Batting rankings at number 31 (November 2013), putting him in the company of Brian Lara (ranked 23), Sachin Tendulkar (29), Steve Waugh (equal 31 with Flower on 895 points) and Rahul Dravid (33).

His aggregate score of 341 in the first Test against South Africa in 2001 is the second highest ever by a batsman on the losing side.

Andy Flower is also the only player to score an ODI hundred on debut in a world cup match. He also has the record for the most number of matches(149) to score his second ODI ton after scoring a century on debut, when he did it in only in his 150th ODI.

He also holds the record for the highest ever test score posted by a wicketkeeper batsman in an innings of a test(232*).

He along with Heath Streak set the record for the highest 7th wicket partnership for Zimbabwe in ODIs(130)