The rights group said it had been able to document 14 civilians killed in investigations of just five airstrikes, a tiny fraction of at least 110 such strikes that the US military says it has launched since June, 2017.
The US military rejected Amnesty's report. It says it has killed 800 militants in airstrikes in Somalia over that period, but has not wounded or killed a single civilian.
"We currently assesses no civilian casualties have occurred as a result of any US Africa Command airstrikes," the US military's Africa command AFRICOM said in en emailed response to Reuters.
Brian Castner, Amnesty International's Senior Crisis Advisor on Arms and Military Operations, said the civilian death toll in the small number of airstrikes the rights group was able to investigate suggested that the "shroud of secrecy surrounding the US role in Somalia's war is actually a smokescreen for impunity".
"Members of the US government forces who planned and carried out the airstrikes may have committed violations of international humanitarian law, including unlawful killings, which could amount to war crimes," Amnesty's report said.
Somalia, one of the poorest countries in the world, has been in a state of civil war and profound insecurity since 1991. In recent years, the US military has been supporting a UN-backed government in Mogadishu fighting against an insurgency by the Al Shabaab group.
In March 2017, President Donald Trump gave the military greater authority to carry out strikes and raids in Somalia, including without waiting for militants to attack US allies.
In a statement, AFRICOM, said: "We have processes in place to ensure the safety and protection of the local population remains a top priority. These procedures, combined with precision strike capabilities, safeguard civilians and infrastructure."
A US airstrike this week killed four people -- an employee of mobile phone company Hormuud Telecoms and three unidentified passengers -- a relative of one of the victims told Reuters on Tuesday.
AFRICOM said it had killed three militants in an airstrike on Monday, adding it was aware of reports alleging civilian casualties and would review the information about the incident.
Amnesty's report investigated five airstrikes in Lower Shabelle region. It concluded that 14 civilians had died and eight were injured.
Al Shabaab was pushed out of the capital Mogadishu in 2011, but retains a strong presence in parts of southern and central Somalia. The militants said US attacks inflict damage on local residents and encourage relatives of victims to join them.
"US strikes target farmers and pastoralists many times in many places of Somalia. People and their farms and animals perish. Their houses get burned," Abdiasis Abu Musab, an Al Shabaab spokesman, told Reuters on Tuesday.